Characterizations of Recently Introduced Univariate Continuous Distributions

G.G. Hamedani and Mehdi Maadooliat
Department of Mathematics, Statistics and Computer Science, Marquette University, WI, USM

Series: Mathematics Research Developments
BISAC: MAT029000

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This monograph is, as far as the authors have gathered, the first one of its kind which presents various characterizations of many important and continuous distributions. It consists of six chapters. The first chapter lists cumulative distribution functions, probability density functions, hazard functions and reverse hazard functions of one hundred thirty-six important univariate continuous distributions. Chapter Two provides characterizations of these distributions based on the ratio of two truncated moments.

Chapter Three takes up the characterizations of some of these distributions in terms of their hazard functions. Chapter Four deals with the characterizations of some of these distributions based on their reverse hazard functions. Characterizations of some of these distributions based on the conditional expectations of certain functions of the random variable are presented in Chapter Five. Finally, to make this book self-contained, we present the characterizations of a large number of distributions (without their proofs) that have already been published by Hamedani and coauthors in Chapter Six.

Chapter 1. Introduction

Chapter 2. Characterizations Based on Two Truncated Moments

Chapter 3. Characterizations Based on Hazard Function

Chapter 4. Characterizations Based on Reverse Hazard Function

Chapter 5. Characterizations Based on Conditional Expectation

Chapter 6. Characterization Results Already Published by Hamedani and Coauthors

References

About the Authors

Index

"The authors have put in tremendous intellectual efforts to come up with this compilation and it will undoubtedly serve as an Encyclopedia in this field of study. It is an amazing compilation of so many basic and derived (life) distributions and their characterizations. As we know characterization problems are themselves very intriguing and intellectually challenging. The authors have mastered the subject matter so much so that they have ventured into this difficult area in presenting a vast material with utmost technical competence. On behalf of the researchers in the area of life distributions and allied topics, I congratulate the authors. Simply told, this is a 'Masterpiece' in any sense of the term." - Bikas K. Sinha, Professor of Statistics (Retired), Indian Statistical Institute, Kolkata, India

“To fully appreciate the meaning and the proper application of a continuous univariate distribution one should be equipped to go through two scientific steps: First Step: one should know the true meaning of the distribution by various available means of characterizations. Second Step: one should know the underlying phenomenon for which the distribution is to be meaningfully approximated. This outstanding book prepared by Professors G.G. Hamedani and M. Maadooliat is providing timely and most comprehensive mathematical/statistical tools for the First Step in applying and utilizing continuous univariate distributions.” - Samad Hedayat, UIC Distinguished Professor, Deptartment of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, Illinois USA

"This volume will be of great value to researchers as they navigate the burgeoning literature on generalized univariate distributions. It will enable them to ruminate on possible variations of existing themes and to avoid rediscovering the wheel in some instances." - Barry Charles Arnold, Distinguished Professor, Department of Statistics, University of California, Riverside, CA USA

"The excellent book of Professors G.G. Hamedani and M. Maadooliat is devoted to characterizations of a large number of recently published continuous univariate distributions. It covers characterizations of 136 recently published continuous univariate distributions. These characterizations are based on the ratio of two truncated moments, the hazard functions, the reverse hazard functions and the conditional expectations of certain functions. Beside these results, important results of the authors of this book and their coauthors in the published papers are given at the end of the book. It is a well-written and easy to read book and represents an up-to-date good source of information for students and researchers who want to learn and work in distribution theory." - Miroslav M. Ristic, Professor, Department of Mathematics, University of Nis, Serbia

Abd El-Monsef, M. M. E. (2016). A new Lindley distribution with location parameter. Communications in Statistics - Theory and Methods, 45:5204–5219.
Abd-Elrahman, A. M. (2014). A new two-parameter lifetime distribution with bathtub, up-bathtub or increasing failure rate function. Journal of Statistics Applications & Probability, 3:21–32.
Abdul-Moniem, I. B. and Seham, M. (2015). Transmuted Gompertz distribution. Computational and Applied Mathematics Journal, 1:88–96.
Adamidis, K. and Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics and Probability Letters, 39:35–42.
Adelfattah, A. M. (2015). Skew-type I generalized Logistic distribution and its properties. Pakistan Journal of Statistics and Operation Research, 11:267–282.
Afify, A. Z., Cordeiro, G. M., Ortega, E. M. M., Yousof, H. M., and Butt, N. S. (2017a). The four-parameter Burr XII distribution: Properties, regression model and applications. Communications in Statistics - Theory and Methods, To appear.
Afify, A. Z., Cordeiro, G. M., Yousof, H. M., Alzaatreh, A., and Nofal, Z. M. (2016a). The Kumaraswamy Transmuted-G family of distributions: Properties and applications. Journal of Data Science, 14:245–270.
Afify, A. Z., Cordeiro, G. M., Yousof, H. M., Saboor, A., and Ortega, E. M. M. (2017b). The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate. Hacettepe Journal of Mathematics and Statistics,To appear.
Afify, A. Z., Hamedani, G. G., Ghosh, I., and Mead, M. E. (2015a). The Transmuted Marshall-Olkin Fréchet distribution: Properties and applications. International Journal of Statistics and Probability,4:132–148.
Afify, A. Z., Nofal, Z. M., and Butt, N. S. (2014). Transmuted complementary Weibull Geometric distribution. Pakistan Journal of Statistics and Operation Research, 10:369– 388.
Afify, A. Z., Nofal, Z. M., and Ebraheim, A. E. H. N. (2015b). Exponentiated Transmuted generalized Rayleigh distribution: A new four parameter Rayleigh distribution. Pakistan Journal of Statistics and Operation Research, 11:115–134.
Afify, A. Z., Nofal, Z. M., Yousof, H. M., El Gebaly, Y. M., and Butt, N. S. (2015c). The Transmuted Weibull-Lomax distribution: Properties and application. Pakistan Journal of Statistics and Operation Research, 11:135–152.
Afify, A. Z., Yousof, H. M., Cordeiro, G. M., Ortega, E. M. M., and Nofal, Z. M. (2016b). The Weibull Fréchet distribution and its applications. Journal of Applied Statistics, 43:2608–2626.
Afify, A. Z., Yousof, H. M., Hamedani, G. G., and Aryal, G. (2016c). The exponentiated Weibull-Pareto distribution with application. Journal of Statistical Theory and Applications, 15:326 – 344.
Agarwal, S. K. and Kalla, S. K. (1996). A generalized Gamma distribution and its application in reliability. Communications in Statistics - Theory and Methods, 25:201210.
Ahmad, A., Ahmad, S. P., and Ahmed, A. (2016). Length-biased weighted Lomax distribution: Statistical properties and application. Pakistan Journal of Statistics and Operation Research, 12:245–255.
Ahmed, M. A., Mahmoud, M. R., and El-Sherpieny, E. A. (2016). The new Kumaraswamy Kumaraswamy Weibull distribution with application. Pakistan Journal of Statistics and Operation Research, 12:165–184.
Ahsanullah, M., Alzaatreh, A., Ghosh, I., and Hamedani, G. G. (2015). Characterizations of the Weibull-X and Burr XII Negative Binomial families of distributions. International Journal of Statistics and Probability, 4:113–122.
Ahsanullah, M., Hamedani, G. G., Kibria, B. M. G., and Shakil, M. (2014). On characterizations of certain continuous distributions. Journal of Statistics,21:75–89.
Akinsete, A., Famoye, F., and Lee, C. (2008). The Beta-Pareto distribution. Statistics, 42:547–563.
Al-Aqtash, R., Lee, C., and Famoye, F. (2014). Gumbel-Weibull distribution: Properties and applications. Journal of Modern Applied Statistical Methods, 13:201–2025.
Al-Babtain, A. A., Eid, A. M., Ahmed, A. H. N., and Merovci, F. (2015a). The five parameter Lindley distribution. Pakistan Journal of Statistics,31:363–384.
Al-Babtain, A. A., Merovci, F., and I., E. (2015b). The McDonald exponentiated Gamma distribution and its statistical properties. SpringerPlus,4:1–22.
Al-Saiari, A. Y., Mousa, S. A., and Baharith, L. A. (2016). Marshall-Olkin extended Burr III distribution. International Mathematical Forum, 11:631–642.
Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S., and Q., S. M. (2016). ToppLeone family of distributions: Some properties and application. Pakistan Journal of Statistics and Operation Research, 12:443–451.
Al-Zahrani, B., Marinho, P. R. D., Fattah, A. A., Ahmed, A.-H. N., and Cordeiro, G. M. (2016). The (P-A-L) extended Weibull distribution: A new generalization of the Weibull distribution. Hacettepe Journal of Mathematics and Statistics, 45:851–868.
Alexander, C., Cordeiro, G. M., Ortega, E. M. M., and Sarbia, J. M. (2012). Generalized Beta-generated distributions. Computational Statistics and Data Analysis,56:1880– 1897.
Ali, A., Hasnain, S. A., and Ahmad, M. (2015). Modified Burr III distribution, properties and applications. Pakistan Journal of Statistics, 31:697–708.
Ali, M. M., Pal, M., and Woo, J. (2012). Estimation of P(Y < X) in a four-parameter generalized Gamma distribution. Austrian Journal of Statistics, 41:197–210.
Alizadeh, M., Cordeiro, G. M., de Brito, E., and Demétrio, C. G. (2015a). The Beta Marshall-Olkin family of distributions. Journal of Statistical Distributions and Applications, 2:1–18.
Alizadeh, M., Emadi, M., and Doostparast, M. (2016a). The odd log-Logistic Marshall-Olkin family of distributions, properties and applications. Personal Communication.
Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G. M., Ortega, E. M. M., and Pescim, R. R. (2015b). A new family of distributions: The Kumaraswamy odd log-Logistic, properties and applications. Hacettepe Journal of Mathematics and Statistics, 44:1491– 1512.
Alizadeh, M., Emadi, M., Doostparast, M., Tahir, M. H., Mansoor, M., and Cordeiro, G. M. (2016b). The odd Fre´chet-G family of distributions. Personal Communication.
Alizadeh, M., Tahir, M., Cordeiro, G. M., Mansoor, M., Zubair, M., and Hamedani, G. G. (2015c). The Kumaraswamy Marshal-Olkin family of distributions. Journal of the Egyptian Mathematical Society, 23:546–557.
Aljarrah, M., Famoye, F., and Lee, C. (2015). A new Weibull-Pareto distribution. Communications in Statistics - Theory and Methods, 44:4077–4095.
Alshawarbeh, E., Famoye, F., and Lee, C. (2013). Beta-Cauchy distribution: Some properties and applications. Journal of Statistical Theory and Applications, 12:378–391.
Alzaatreh, A., Famoye, F., and Lee, C. (2012). Gamma-Pareto distribution and its applications. Journal of Modern Applied Statistical Methods, 11:78–94.
Alzaatreh, A., Famoye, F., and Lee, C. (2013a). Weibull-Pareto distribution and its applications. Communications in Statistics - Theory and Methods, 42:1673–1691.
Alzaatreh, A. and Ghosh, I. (2015). On the Weibull-X family of distributions. Journal of Statistical Theory and Applications, 14:169–183.
Alzaatreh, A. and Ghosh, I. (2016). A study of the Gamma-Pareto (IV) distribution and its applications. Communications in Statistics - Theory and Methods, 45:636–654.
Alzaatreh, A., Ghosh, I., and Said, H. (2014). On the Gamma-Logistic distribution. Journal of Modern Applied Statistical Methods, 13:55–70.
Alzaatreh, A., Lee, C., and Famoye, F. (2013b). A new method for generating families of continuous distributions. Metron, 71:63–79.
Alzaatreh, A., Mansoor, M., Tahir, M. H., Zubair, M., and Ghazali, S. A. (2015). The Gamma half-Cauchy distribution: Properties and applications. In Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics.
Alzaghal, A., Ghosh, I., and Alzaatreh, A. (2016). On shifted Weibull-Pareto distribution. International Journal of Statistics and Probability, 5:139–149.
Amini, M., Mirmostafaee, S. M. T. K., and Ahmadi, J. (2012). Log-Gamma-generated families of distributions. Statistics, iFirst:1–20.
Aryal, G. R. (2013). Transmuted log-Logistic distribution. Journal of Statistics Applications & Probability, 2:11–20.
Asadi, M., Ebrahimi, N., Hamedani, G. G., and Soofi, E. S. (2004). Maximum dynamic entropy models. Journal of Applied Probability, 41:379–390.
Asadi, M., Ebrahimi, N., Hamedani, G. G., and Soofi, E. S. (2005). Minimum dynamic discrimination information models. Journal of Applied Probability, 42:643–660.
Asgharzadeh, A., Bourguignon, M., and Ghorbanzadeh, M. (2016). The generalized inverse Nadarajah-Haghighi distribution. Journal of Statistics Applications & Probability, Submitted.
Batsidis, A. and Lemonte, A. J. (2015). On Harris extended family of distributions. Statistics, 49:1400–1421.
Behboodian, J., Jamalizadeh, A., and Balakrishnan, N.(2006). A new class of skew-Cauchy distributions. Statistics, 76:1488–1493.
Bidram, H., Alamatsaz, M. H., and Nekoukhou, V. (2015). On an extension of the exponentiated Weibull distribution. Communications in Statistics - Simulation and Computation, 44:1389–1404.
Bidram, H., Behboodian, J., and Towhidi, M. (2013a). A new generalized Exponential Geometric distribution. Communications in Statistics - Theory and Methods, 42(3):528– 542.
Bidram, H., Behboodian, J., and Towhidi, M. (2013b). The Beta Weibull-Geometric distribution. Journal of Statistical Computation and Simulation, 83:52–67.
Bílková, D. and Malá, I. (2012). Modelling the income distributions in the Czech Republic since 1992. Austrian Journal of Statistics, 41:133–152.
Birnbaum, Z. W. and Saunders, S. C. (1969). A new family of life distributions. Journal of Applied Probability, 6:319–327.
Bondesson, L. (1979). A general result on infinite divisibility. The Annals of Probability, 7:965–979.
Bondesson, L. (1992). Generalized Gamma convolutions and related classes of distributions and densities. Lecture notes in statistics. Springer-Verlag, New York.
Bordbar, F. and Nematollahi, A. R. (2016). The modified Exponential-Geometric distribution. Communications in Statistics - Theory and Methods, 45:173–181.
Bourguignon, M., Ghosh, I., and Cordeiro, G. M. (2016). General results for the Transmuted family of distributions and new models. Journal of Probability and Statistics, Article ID 7208425:1–12.
Bourguignon, M., Lima, M. D. S., Leão, J., Nascimento, A. D. C., Pinho, L. G. B., and Cordeiro, G. M. (2015). A new generalized Gamma distribution with applications. American Journal of Management Sciences, 14:20–34.
Bourguignon, M., Silva, R. B., and Cordeiro, G. M. (2014). The Weibull-G family of probability distributions. Journal of Data Science, 12:53–68.
Bourguignon, M., Silva, R. B., Zea, L. M., and Zea Cordeiro, G. M. (2013). The Kumaraswamy Pareto distribution. Journal of Statistical Theory and Applications, 12:129– 144.
Carrasco, J. M. F., Ortega, E. M. M., and Cordeiro, G. M. (2008a). A generalized modified Weibull regression models with censored data: Sensitivity and residual analysis. Computational Statistics and Data Analysis, 52:4021–4039.
Carrasco, J. M. F., Ortega, E. M. M., and Paula, G. A. (2008b). Log-modified Weibull distribution for lifetime modeling. Computational Statistics and Data Analysis, 53:450– 462.
Castellars, F. and Lemonte, A. (2015). A new generalized Weibull distribution generated by Gamma random variables. Journal of the Egyptian Mathematical Society, 23:382–390.
Chakraborty, S., Hazarika, P. J., and Ali, M. M. (2012). A new skew Logistic distribution and its properties. Pakistan Journal of Statistics, 28:513–524.
Cordeiro, G., Silva, G., and Ortega, E. (2016a). An extended-G geometric family. Journal of Statistical Distributions and Applications, 3:3:1–16.
Cordeiro, G. M., Alizadeh, M., and Ortega, E. M. M. (2014a). The exponentiated half-Logistic family of distributions: Properties and applications. Journal of Probability and Statistics, Article ID 864396:1–21.
Cordeiro, G. M., Alizadeh, M., Ortega, E. M. M., and Serrano, L. H. V. (2016b). The Zografos-Balakrishnan odd log-Logistic family of distributions: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 45:1781–1803.
Cordeiro, G. M., Braga Junior, A. C. R., Demétrio, C. G. B., Ortega, E. M. M., and Pescim, R. R. (2014b). Some new results for the Kumaraswamy modified Weibull distribution. Journal of Statistical Theory and Applications, 13:86–104.
Cordeiro, G. M. and Brito, R. D. S. (2012). The Beta power distributions. Brazilian Journal of Probability and Statistics, 26:88–112.
Cordeiro, G. M., Cancho, V. G., Ortega, E. M. M., and Barriga, G. D. C. (2016c). A model with long-term survivors: Negative Binomial Birnbaum-Saunders. Communications in Statistics - Theory and Methods, 45:1370–1387.
Cordeiro, G. M. and de Castro M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81:883–898.
Cordeiro, G. M., Hashimoto,E. M., and Ortega, E. M. M. (2014c). The McDonald Weibull model. Statistics, 48:256–278.
Cordeiro, G. M., Lima, M. C. S., Gomes, A. E., da Silva, C. Q., and Ortega, E. M. M. (2016d). The Gamma extended Weibull distribution. Journal of Statistical Distributions and Applications, 3:1–18.
Cordeiro, G. M., Nadarajah, S., and Ortega, E. M. M. (2012). The Kumaraswamy Gumbel distribution. Statistical Methods and Applications, 21:139–168.
Cordeiro, G. M., Ortega, E. M. M., and da Cunha, D. C. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11:1–27.
Cordeiro, G. M., Ortega, E. M. M., and Lemonte, A. (2015a). The Poisson generalized linear failure rate model. Communications in Statistics - Theory and Methods, 44:2037– 2058.
Cordeiro, G. M., Ortega, E. M. M., and Popović, B. V. (2015b). The gamma-Lomax distribution. Journal of Statistical Computation and Simulation, 85:305–319.
Cordeiro, G. M., Ortega, E. M. M., and Ramires, T. (2015c). A new generalized Weibull family of distributions: Mathematical properties and applications. Journal of Statistical Distributions and Applications, 2:1–25.
Cordeiro, G. M., Ortega, E. M. M., and Silva, O. G. (2011). The exponentiated generalized Gamma distributionwith applicationto lifetime data. Journal of Statistical Computation and Simulation, 81:827–842.
Cordeiro, G. M., Pescim, R. R., Demétrio, C. G. B., and Ortega, E. M. M. (2014d). The Kummer Beta generalized Gamma distribution. Journal of Data Science, 12:661–698.
Cordeiro, G. M., Ramires, T. G., Ortega, E. M. M., and Alizadeh, M. (2016e). The new family of distributions and applications in heteroscedastic regression analysis. Submitted.
Cordeiro, G. M., Saboor, A., Khan, M. N., Ozel, G., and Pascoa, M. A. R. (2016f). The Kumaraswamy exponential-Weibull distribution: Theory and applications. Hacettepe Journal of Mathematics and Statistics, 45:1203–1229.
Cordeiro, G. M., Silva, G. O., and Ortega, E. (2016g). An extended-G geometric distribution. Journal of Statistical Distributions and Applications, 3:3:1–16.
Crooks, G. E. (2010). The Amoroso distribution. arXiv preprint arXiv:1005.3274.
da Silva, M. A. R., Gomes-Silva, F., Ramos, M. W. A., and Cordeiro, G. M. (2015a). The exponentitaed Burr XII Poisson distribution with application to lifetime data. International Journal of Statistics and Probability, 4:112–131.
da Silva, R. C., Sanchez, J. J. D., Lima, F. P., and Cordeiro, G. M. (2015b). The Kumaraswamy Gompertz distribution. Journal of Data Science, 13:241–260.
da Silva, R. V., de Andrade, T. A. N., Maciel, D. B. M., Campos, R. P. S., and Cordeiro, G. M. (2013). A new lifetime model: The gamma extended Fréchet distribution. Journal of Statistical Theory and Applications, 12:39–54.
Danish, M. Y. and Aslam, M. (2013). Bayesian analysis of randomly censored generalized Exponential distribution. Austrian Journal of Statistics, 42:47–62.
de Andrade, T. A. N., Bourguignon, M., and Cordeiro, G. M. (2016). The exponentiated generalized extended Exponential distribution. Journal of Data Science, 14:393–414.
de Brito, E., Silva, G. O., and Cordeiro, G. M. (2016). The McDonald Gumbel distribution. Communications in Statistics - Theory and Methods, 45:3367–3382.
de Pascoa, R. V., Ortega, E. M. M., and Cordeiro, G. M. (2011). The Kumaraswamy generalized Gamma distribution with applicationin survival analysis. Statistical Methodology, 8:411–433.
de Santana, T. V. F., Ortega, E. M. M., Cordeiro, G. M., and Silva, G. O. (2012). The Kumaraswamy-log-Logistic distribution. Journal of Statistical Theory and Applications, 11:265–291.
Domma, F. and Condino, F. (2013). The Beta-Dagum distribution: Definition and properties. Communications in Statistics - Theory and Methods, 42:4070–4090.
Domma, F. and Perri, P. F. (2009). Some development on the log-Dagum distribution. Statistical Methods and Applications, 18:205–220.
Doostmardi, A., Zadkarami, M. R., and Roshani Sheykhabad, A. (2014). A new modified Weibull distribution and its applications. Journal of Statistical Research of Iran, 11:97– 118.
El-Bassiouny, A. H., El-Damcese, M., Mustafa, A., and Eliwa, M. S. (2015). Characterizations of the generalized Weibull-Gompertz distribution based on the upper record values. International Journal of Mathematics and its Applications, 3:13–22.
El-Damcese, M. A., Mustafa, A., El-Desouky, B. S., and Mustafa, M. E. (2016a). The Kumaraswamy flexible Weibull extension. International Journal of Mathematics and its Applications, 4:1–14.
El-Damcese, M. A., Mustafa, A., and Eliwa, M. S. (2016b). Exponentiated generalized Weibull-Gompertz distribution. Personal Communication.
El-Gohary, A., El-Bassiouny, A. H., and El-Morshedy, M. (2015a). Exponentiated flexible Weibull Extension distribution. International Journal of Mathematics and its Applications, 3:1–12.
El-Gohary, A., El-Bassiouny,A. H., and El-Morshedy,M. (2015b). Inverse flexible Weibull extension distribution. International Journal of Computer Applications, 115:46–51.
El-Sherpieny, E. A. and Ahmed, M. A. (2014). On the Kumaraswamy Kumaraswamy distribution. Journal of Basic and Applied Sciences, 3:372–381.
Elbatal,I. (2013). The Kumaraswamy exponentiated Pareto distribution. Economic Quality Control, 28:1–8.
Elbatal, I. and Aryal, G. (2013). On the Transmuted additive Weibull distribution. Austrian Journal of Statistics, 42:117–132.
Elbatal, I., Diab, L. S., and Abdul Alim, N. A. (2013a). Transmuted generalized linear Exponential distribution. International Journal of Computer Applications, 83:29–37.
Elbatal, I. and Elgarhy, M. (2013). Statistical properties of Kumaraswamy Quasi Lindley distribution. International Journal of Mathematics Trends and Technology, 4:237–246.
Elbatal, I., Mansour, M. M., and Ahsanullah, M. (2016). The additive Weibull-Geometric distribution: Theory and Applications. Journal of Statistical Theory and Applications, 15:125–141.
Elbatal, I., Merovci, F., and Elgarhy, M. (2013b). A new generalized Lindley distribution. Mathematical Theory and Modeling, 3:30–47.
Elbatal, I., Merovci, F., and Marzouk, W. (2014). McDonald generalized linear failure rate distribution. Pakistan Journal of Statistics and Operation Research, 10:267–288.
Eugene, N., Lee, C., and Famoye, F. (2002). Beta-Normal distribution and its applications. Communications in Statistics - Theory and Methods, 31:497–512.
Fatima, A. and Roohi, A. (2015). Extended Poisson exponentiated distribution. Pakistan Journal of Statistics and Operation Research, 11:361–375.
Fatima, A. and Roohi, A. (2016). Transmuted exponentiated Pareto-I distribution. Pakistan Journal of Statistics, 32:63–80.
Feroze, N. and Elbatal, I. (2016). Beta exponentiated gamma distribution: Some properties and estimation. Pakistan Journal of Statistics and Operation Research, 12:141–154.
Fioruci, J., Yiqi, B., Louzada, F., and Cancho, V. G. (2016). The exponential Poisson logarithmic distribution. Communications in Statistics - Theory and Methods, 45:2556– 2575.
Galambos, J. and Kotz, S. (1978). Characterizations of probability distributions. A unified approach with an emphasis on Exponential and related models, volume 675 of Lecture Notes in Mathematics. Springer, New York.
Garc´ia, V., Gómez-déniz, E., and Vázquez-polo, F. J. (2016). Marshall-Olkin family of heavy-tailed distributions which includes the Lognormal one. Communications in Statistics - Theory and Methods, 45:2023–2044.
Ghitany, M. E., Al-Awadhi, F. A., and Alkhalfan, L. A. (2007). Marshall-Olkin extended Lomax distribution and its application to censored data. Communications in Statistics Theory and Methods, 36:1855–1866.
Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., and Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64:20–33.
Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K., and Husain, H. A. (2011). A two-parameter weighted Lindley distribution and its applications to survival data. Mathematics and Computers in Simulation, 81:1190–1201.
Ghosh, I. (2014). The Kumaraswamy-half-Cauchy distribution: Properties and application. Journal of Statistical Theory and Applications, 13:122–134.
Ghosh, I. and Alzaatreh, A. (2017). A new class of generalized Logistic distribution. Communications in Statistics - Theory and Methods, To appear.
Ghosh, I. and Bourguignon, M. (2017). A new extended Burr XII distribution. Austrian Journal of Statistics, page Submitted.
Glänzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), B:75–84.
Glänzel, W. (1988). A characterization of the Normal distribution. Studia Scientiarum Mathematicarum Hungarica, 23:89–91.
Glänzel, W. (1990). Some consequences of a characterization theorem based on truncated moments. Statistics, 21:613–618.
Glänzel, W. (1994). IrWin - A characterization tool for discrete distributions under Windows(R). In Dutter, R. and Grossman, W., editors, COMPSTAT, Short Communications in Computational Statistics.
Glänzel, W. and Hamedani, G. G. (2001). Characterizations of univariate continuous distributions. Studia Scientiarum Mathematicarum Hungarica, 37:83–118.
Glänzel,W., Telcs,A., and Schubert, A.(1984). Characterization by truncated moments and its application to Pearson-type distributions. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 66:173–183.
Gomes, A. E., Da-Silva, C. Q., and Cordeiro, G. M. (2015a). The exponentiated G Poisson model. Communications in Statistics - Theory and Methods, 44:4217–4240.
Gomes, A. E., da Silva, C. Q., and Cordeiro, G. M. (2015b). Two extended Burr models: Theory and practice. Communications in Statistics- Theory and Methods,44:1706–1734.
Gómez-Déniz, E., Calderín-Ojeda, E., and Sarabia, J. M. (2013). Gamma-generalized inverse Gaussian class of distributions with applications. Communications in Statistics Theory and Methods, 42:919–933.
Gompertz, B. (1825). On the nature of the function expressive of the Law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115:513–583.
Granzotto, D. C. T. and Louzada, F. (2015). The Transmuted log-Logistic distribution: Modeling, inference, and an application to a polled Tabapua race time up to first calving data. Communications in Statistics - Theory and Methods, 44:3387–3402.
Gupta, R. C., Gupta, R. D., and Gupta, P. L. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics - Theory and Methods, 27:887–904.
Hakamipour, N., Nadarajah, S., and Rezaei, S. (2012). Logarithmic mixture distribution. Personal Communication.
Hamedani, G. G. (1993). Characterizations of Cauchy, Normal and Uniform distributions. Studia Scientiarum Mathematicarum Hungarica, 28:243–247.
Hamedani, G. G. (2002). Characterizations of univariate continuous distributions

II. Studia Scientiarum Mathematicarum Hungarica, 39:407–424.
Hamedani, G. G. (2004). Characterizations of univariate continuous distributions based on hazard functions. Journal of Applied Statistical Science, 13:169–183.
Hamedani, G. G. (2006). Characterizations of univariate continuous distributions

III. Studia Scientiarum Mathematicarum Hungarica, 43:361–385.
Hamedani, G. G. (2010). Characterizations of continuous univariate distributions based on the truncated moments of functions of order statistics. Studia Scientiarum Mathematicarum Hungarica, 47:462–484.
Hamedani, G. G. (2011). Characterizations of the Shakil-Kibria-Singh Distribution. Austrian Journal of Statistics, 40:201–207.
Hamedani, G. G. (2012a). Characterizations of the Amoroso distribution. Studia Scientiarum Mathematicarum Hungarica, 49:338–347.
Hamedani, G. G. (2012b). Various characterizations of modified Weibull and log-modified Weibull distributions. Austrian Journal of Statistics, 41:117–124.
Hamedani, G. G. (2013a). Characterizations of certain continuous distributions, multiscale signal analysis and modeling. Springer, New York.
Hamedani, G. G. (2013b). Characterizations of certain recently introduced distributions. Journal of Statistical Theory and Applications, 12:11–20.
Hamedani, G. G. (2013c). Characterizations of distribution of ratio of Rayleigh random variables. Pakistan Journal of Statistics, 29:369–376.
Hamedani, G. G. (2013d). Characterizations of distributions of ratio of certain independent random variables. Journal of Applied Mathematics, Statistics and Informatics,9:15–25.
Hamedani, G. G. (2013e). Characterizations of exponentiated distributions. Pakistan Journal of Statistics, 1:17–24.
Hamedani, G. G. (2013f). On certain generalized Gamma convolution distributions

II. Technical Report 484, MSCS, Marquette University.
Hamedani, G. G. (2013g). On generalized Gamma convolution distributions. Journal of Applied Mathematics, Statistics and Informatics, 9:5–14.
Hamedani, G. G. (2014a). Characterizations of new modified Weibull distribution. Journal of Statistical Research of Iran, 11:223–229.
Hamedani, G. G. (2014b). On characterizations of randomly censored generalized Exponential distribution. Journal of Applied Mathematics, Statistics and Informatics, 10:85– 92.
Hamedani, G. G. (2015a). A short note on characterizations of Kumaraswamy Kumaraswamy distribution. International Journal of Basic and Applied Science, 3:61–64.
Hamedani, G. G. (2015b). Characterizations of Kumaraswamy Fréchet distribution. Australian Journal of Basic and Applied Sciences, 9:995–998.
Hamedani, G. G. (2015c). Characterizations of NWP, ETGR and TWL distributions. Pakistan Journal of Statistics and Operation Research, 11:473–480.
Hamedani, G. G. (2015d). Characterizations of Transmuted complementary Weibull Geometric distribution. Pakistan Journal of Statistics and Operation Research, 11:153–157.
Hamedani,G.G.(2016). On characterizations and infinite divisibility of recently introduced distributions. Studia Scientiarum Mathematicarum Hungarica, 53:467–511.
Hamedani, G. G. and Ahsanullah, M. (2005). Characterizations of univariate continuous distributions based on hazard functions

II. Journal of Statistical Theory and Applications, 4:218–238.
Hamedani, G. G. and Ahsanullah, M. (2011). Characterizations of Weibull Geometric distribution. Journal of Statistical Theory and Applications, 10:581–590.
Hamedani, G. G.and Gosh,I. (2015). Kumaraswamy-half-Cauchy distribution: Characterizations and related results. International Journal of Statistics and Probability, 4:94–100.
Hamedani, G. G. and Najibi, S. M. (2016). The Transmuted exponentiated generalized-G family of distributions. Pakistan Journal of Statistics and Operation Research, 12:551– 577.
Hanagal, D. D. and Pandey, A. (2014). Gamma shared frailty model based on reversed hazard rate for bivariate survival data. Statistics and Probability Letters, 88:190–196.
Hashimoto, E. M., Ortega, E. M. M., Cancho, V. G., and Cordeiro, G. M. (2010). The log-exponentiated Weibull regression model for interval-censored data. Computational Statistics and Data Analysis, 54:1017–1035.
Hassanein, W. A. and Elhaddad, T. A. (2016). Truncated Lindley Gamma distribution. Pakistan Journal of Statistics, 32:227–246.
Haung, S. and Oluyede, B. (2014). Exponentiated Kumaraswamy-Dangum distribution with applications to income and lifetime data. Journal of Statistical Distributions and Applications, 1:1–20.
Iqbal, Z., Hasania, S. A., Salman, M. A., and Hamedani, G. G. (2014). Generalized exponentiated moment Exponential distribution. Pakistan Journal of Statistics, 30:537–554.
Jafari, A. A., Tahmasebi, S., and Alizadeh, M. (2014). The Beta-Gompretz distribution. Revista Colombiana de Estadistica, 37:139–156.
Javanshiri,Z., A., H. R., and Hamedani, G.G.(2013). Exp-Uniform distribution: Properties and characterizations. Journal of Statistical Research of Iran, 10:85–106.
Javanshiri, Z., Habibi Rad, A., and Arghami, N. R. (2015). Exp-Kumaraswamy distributions: Some properties and applications. Jornal of Sciences (Islamic Republic of Iran), 26:57–69.
Johnson,N. L., Kotz, S., and Balakrishnan,N. (1994). Continuous univariate distributions, volume 1 and 2. John Wiley, New York, 2nd edition.
Jose, K. K. and Sivadas, R.(2015). Harrisextended Burr XII and exponentiated Exponential distribution. Personal Communication.
Kadilar, G. (2014). Kumaraswamy generalized Exponential Weibull distribution. Young Women in Probability.
Khan, H. M. R. (2014a). On predictive inference from the compound Rayleigh model based on censored samples. Pakistan Journal of Statistics, 14:21–34.
Khan, M. N. (2016). The modified beta Weibull distribution with applications. Hacettepe Journal of Mathematics and Statistics, 44:1553–1568.
Khan, M. S. (2014b). Modified inverse Rayleigh distribution. International Journal of Computer Application, 87:28–33.
Khan, M. S. and King, R. (2012). Modified inverse Weibull distribution. Journal of Statistics Applications & Probability, 1:115–132.
Khan, M. S. and King, R. (2015). Transmuted modified inverse Rayleigh distribution. Austrian Journal of Statistics, 44:17–29.
Khan, M. S. and King, R. (2016). New generalized inverse Weibull distribution for lifetime modeling. Communications for Statistical Applications and Methods, 23:147–161.
Khan, M. S., King, R., and Hudson, I. (2016a). A new three parameter Transmuted Chen lifetime distribution with application. Journal of Applied Statistical Science, 21:239–259.
Khan, M. S., King, R., and Hudson, I. L. (2016b). Three parameter Transmuted Rayleigh distribution with application to Reliability data. Journal of Statistical Theory and Applications, 15:296–312.
Khan, M. S., King, R., and Hudson, I. L. (2016c). Transmuted Gompertz distribution: Properties and estimation. Pakistan Journal of Statistics, 32:161–182.
Kotz, S. and Shanbhag, D. N. (1980). Some new approaches to probability distributions. Advances in Applied Probability, 12:903–921.
Krishna, E., Jose, K. K., and Ristić, M. M. (2013). The Marshall-Olkin Fréchet distribution. Communications in Statistics - Theory and Methods, 42:4091–4107.
Lemonte, A. J. (2014). The Beta log-Logistic distribution. Brazilian Journal of Probability and Statistics, 28:313–332.
Lemonte, A. J. and Cordeiro, G. M.( 2011). The exponentiated generalized inverse Gaussian distribution. Statistics and Probability Letters, 81:506–517.
Lemonte, A. J. and Cordeiro, G. M. (2013). An extended Lomax distribution. Statistics, 47:800–816.
Lemonte, A. J., Cordeiro, G. M., and Ortega, E. M. M. (2014). On the additive Weibull distribution. Communications in Statistics - Theory and Methods, 43:2066–2080.
Lemonte, J., Cordeiro, G. M., and Moreno-Arenas, G.(2016). A new useful three-parameter extension of the Exponential distribution. Communications in Statistics - Theory and Methods, 50:312–337.
Lima, M. C. S., Cordeiro, G. M., and Ortega, E. M. M. (2015). A new extension of the Normal distribution. Journal of Data Science, 13:385–408.
Lima, S. R. and Cordeiro, G. M. (2016). The extended log-Logistic distribution: Properties and application. Submitted.
Ljubo, M. (1965). Curves and concentration indices for certain generalized Pareto distribution. Statistical Review, 15:257–260.
Louzada, F., Marchi, V. A. A., and Roman, M. (2014). The exponentiated Exponential-Geometric distribution: A distribution with decreasing, increasing and unimodal failure rate. Statistics, 48:167–181.
Lucena, S. E. F., Silva, A. H. A., and Cordeiro, G. M. (2015). The Transmuted generalized Gamma distribution: Properties and application. Journal of Data Science, 13:409–420.
Mabrouk, I. (2011). Generalized Exponential models with applications. PhD thesis, University of Western Ontario, Canada.
Mahmoud, M. R., El-Sherpieny, E. A., and Ahmad, M. A. (2015). The new Kumaraswamy Kumaraswamy family of generalized distributions with application. Pakistan Journal of Statistics and Operation Research, 11:159–180.
Mahmoudi, E. (2011). The Beta generalized Pareto distribution with application to lifetime data. Mathematics and Computers in Simulation, 81:2414–2430.
Maiti, S. S. and Pramanik, S. (2015). Odds generalized Exponential-Exponential distribution. Journal of Data Science, 13:733–754.
Maiti, S. S. and Pramanik, S. (2016). Odds generalized Exponential-Pareto distribution: Properties and application. Pakistan Journal of Statistics and Operation Research, 12:257–279.
Mameli, V. and Musio, M. (2013). A generalization of the skew-Normal distribution: The Beta skew-Normal. Communications in Statistics - Theory and Methods, 42:2229–2244.
Mansoor, M., Tahir, M., Alzaatreh, A., Cordeiro, G. M., Zubair, M., and Ghazali, S. S. A. (2016). An extended Fréchet distribution: Properties and applications. Journal of Data Science, 14:167–188.
McDonald, J. B. (1984). Some generalized functions for the size distribution of income. Econometrica, 52:647–665.
Mead, M. E. (2014a). A new generalization of Burr XII distribution. Journal of Statistics: Advances in Theory and Applications, 12:53–73.
Mead, M. E. (2014b). An extended Pareto distribution. Pakistan Journal of Statistics and Operation Research, 10:313–329.
Mead, M. E. (2015). The Kumaraswamy exponentiated Burr XII distribution and its applications. Pakistan Journal of Statistics and Operation Research, 11:138–148.
Mead, M. E. (2016). On five-parameter Lomax distribution: Properties and applications. Pakistan Journal of Statistics and Operation Research, 12:185–199.
Mead, M. E. and Abd-Eltawab, A. R. (2014). A note on Kumaraswamy Fréchet distribution. Australian Journal of Basic and Applied Sciences, 8:294–300.
Mead, M. E. and Egypt, Z. (2015). Generalized inverse Gamma distribution and its application in reliability. Communications in Statistics - Theory and Methods, 44:1426–1435.
Mendoza, N. V. R., Ortega, E. M. M., and Cordeiro, G. M. (2016). The exponentiated-log-Logistic Geometric distribution: Dual activation. Communications in Statistics - Theory and Methods, 45:3838–3859.
Merovci, F. (2013). Transmuted Rayleigh distribution. Austrian Journal of Statistics, 42:21–31.
Merovci, F. (2014). Transmuted generalized Rayleigh distribution. Journal of Statistics Applications & Probability, 3:9–20.
Merovci, F. and Elbatal, I. (2014). Transmuted Lindley-Geometric distribution and its applications. Journal of Statistics Applications & Probability,3:77–91.
Merovci, F. and Elbatal, I. (2015a). A new generalized exponentiated modified Weibull distribution. Journal of Data Science, 13:213–240.
Merovci, F. and Elbatal, I. (2015b). The Beta quadratic hazard rate distribution. Pakistan Journal of Statistics, 31:427–446.
Merovci, F., Elbatal, I., and Ahmed, A. (2014). The Transmuted generalized inverse Weibull distribution. Austrian Journal of Statistics, 43:119–131.
Mirhosseini, S. and Lalehzari, R. (2011). A perturbed Weibull distribution and its application. Personal Communication.
MirMostafaee, S. M. T. K., Mahdizadeh, M., and Lemonte, A. (2017). The Marshall-Olkin extended generalized Rayleigh distribution: Properties and applications. Communications in Statistics - Theory and Methods, 46:635–671.
MirMostafaee, S. M. T. K., Mahdizadeh, M., and Nadarajah, S. (2015). The Beta Lindley distribution. Journal of Data Science, 13:603–626.
Mohie El-Din, M. M., Amein, M. M., and Hamedani, G. G. (2012). On order statistics for GS-distributions. Journal of Statistical Theory and Applications, 11:237–264.
Muhammad, M. (2017). Poisson-odd generalized exponential family of distributions: Theory and applications. Hacettepe Journal of Mathematics and Statistics, To appear.
Mustafa, A., El-Desouky, B. S., and AL-Garash, S. (2016). The Weibull generalized flexible Weibull extension distribution. Journal of Data Science, 14:453–478.
Nadarajah, S. (2008). Some Gamma distributions. Statistics, 42:7794.
Nadarajah, S., Bakouch, H.S., and Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B, 73(331359):331–359.
Nadarajah, S. and Haghighi, F. (2011). An extension of the Exponential distribution. Statistics, 45:543–558.
Nadarajah, S. and Kotz, S. (2006). On the product and ratio of Gamma and Weibull random variables. Econometric Theory, 22(2):338–344.
Nadarajah, S., Nassiri, V., and Mohammadpour, A. (2014a). Truncated-Exponential skew-symmetric distributions. A Journal of Theoretical and Applied Statistics, 48:872–895.
Nadarajah, S., Shahsanei, F., and Rezaei, S. (2014b). A new four-parameter lifetime distribution. Journal of Statistical Computation and Simulation, 84:248–263.
Nascimento, A. D. C., Bourguignon, M., Zea, L. M., Santos-Neto, M., Silva, R. B., and Cordeiro, G. M. (2014). The Gamma extended Weibull family of distributions. Journal of Statistical Theory and Applications, 13:1–16.
Nascimento, F., Bourguignon, M., and Leão, J. (2016). Extended generalized extreme value distribution with applications in environmental data. Hacettepe Journal of Mathematics and Statistics, 45:1847–1864.
Nasiru, S. and Luguterah, A.(2015). The new Weibull-Pareto distribution. Pakistan Journal of Statistics and Operation Research, 11:101–112.
Nassar, M. M. and Nada, N. K. (2011). The Beta generalized Pareto distribution. Journal of Statistics: Advances in Theory and Applications, 6:1–17.
Nasseri, V. and Mohammadpour, A. (2009). Very skewed Cauchy distribution: A new heavy-tailed member of exponential family. Amirkabir, 20:85–92.
Nofal, Z. M., Afify, A. Z., Yousof, H. M., and Cordeiro, G. M. (2017). The generalized Transmuted-G family of distributions. Communications in Statistics - Theory and Methods, To appear.
Nofal, Z. M., Afify, A. Z., Yousof, H. M., Granzoto, D. C. T., and Louzada, F. (2016). Kumaraswamy Transmuted exponentiated additive Weibull distribution. International Journal of Statistics and Probability, 5:78–99.
Oliveira, J., Santos, J., Xavier, C., Trindade, D., and Cordeiro, G.M. (2016). The McDonald half-Logistic distribution: Theory and practice. Communications in Statistics - Theory and Methods, 45:2005–2022.
Oluyede, B., Foya, S., Warahena-Liyanage, G., and Huang, S. (2016a). The log-Logistic Weibull distribution with applications to lifetime data. Austrian Journal of Statistics, 45:43–69.
Oluyede, B. O., Elbatal, I., and Huang, S. (2016b). Beta linear failure rate Geometric distribution with applications. Journal of Data Science, 14:317–346.
Oluyede, B. O., Huang, S., and Pararai, M. (2014). A new class of generalized Dagum distribution with applications to income and lifetime data. Journal of Statistical and Econometric Methods, 3:125–151.
Oluyede, B. O., Huang, S., and Yang, T. (2015a). A new class of generalized modified Weibull distribution with applications. Austrian Journal of Statistics, 44:45–68.
Oluyede, B. O., Mutiso, F., and Huang, S. (2015b). The log generalized Lindley-Weibull distribution with application. Journal of Data Science, 13:281–310.
Oluyede, B. O. and Rajasooriya, S. (2013). The Mc-Dagum distribution and its statistical properties with applications. Asian Journal of Mathematics and Applications, ama0085:1–16.
Oluyede, B. O. and T., Y. (2015). A new class of generalized Lindley distributions with applications. Journal of Statistical Computation and Simulation, 85:2072–2100.
Ortega, E. M. M., Cordeiro, G. M., and Hashimoto, E. M. (2011). A log-linear regression model for the Beta-Weibull distribution. Communications in Statistics - Theory and Methods, 40:1206–1235.
Ortega, E. M. M., Cordeiro, G. M., and Lemonte, A. J. (2012). A log-linear regression model for the β-Birnbaum-Saunders distribution with censored data. Computational Statistics and Data Analysis, 56:698–718.
Ownuk, J. (2015). The Beta exponentiated Gumbel distribution. Journal of the Iranian Statistical Society, 14:1–14.
Pal, M. and Tiensuwan, M. (2014). The Beta Transmuted Weibull distribution. Austrian Journal of Statistics, 43:133–149.
Paranaíba, P. F., Ortega, E. M. M., Cordeiro, G. M., and de Pascoa, M. A. R. (2013). The Kumaraswamy Burr XII distribution: Theory and practice. Journal of Statistical Computation and Simulation, 83:2117–2143.
Paranaíba, P. F., Ortega, E. M. M., Cordeiro, G. M., and Pescim, R. R. (2011). The Beta Burr XII distribution with application to lifetime data. Computational Statistics and Data Analysis, 55:1118–1136.
Pararai, M., Oluyede, B. O., and Warahena-Liyanage, G. (2016). The Beta Lindley-Poisson distribution with applications. Journal of Statistical and Econometric Methods, 5:1–37.
Pescim, R. R., Demétrio, C. G. B., Cordeiro, G. M., Ortega, E. M. M., and Urbano, M. R. (2010). The Beta generalized half-Normal distribution. Computational Statistics and Data Analysis, 54:945–957.
Pescim, R. R. and Nadarajah, S. (2015). The Kummer Beta Normal: A new useful-skew model. Journal of Data Science, 13:509–532.
Pescim, R. R., Ortega, E. M. M., Cordeiro, G. M., Demtrio, C. G. B., and Hamedani, G. G. (2013). The log-Beta generalized half-Normal regression model. Journal of Statistical Theory and Applications, 12:330–347.
Phani, Y., Girija, S. V. S., and Rao, A. V. D. (2013). Arc tan-exponential type distribution induced by stereographic projection/bilinear transformation on modified wrapped Exponential distribution. Journal of Applied Mathematics, Statistics and Informatics, 9:69–74.
Pinho, L., Cordeiro, G., and Nobre, J. (2012). The Gamma-exponentiated Weibull distribution. Journal of Statistical Theory and Applications, 11(4):379–395.
Pinho, L. G., Cordeiro, G. M., and Nober, J. (2015a). The Harris extended exponentiated distribution. Communications in Statistics - Theory and Methods, 44:3489–3502.
Pinho, L. G. B., Cordeiro, G. M., and Nobre, J. S. (2015b). On the Harris-G class of distributions: General results and application. Brazilian Journal of Probability and Statistics, 29:813–832.
Pogány, T. K. (2015). The exponentiated Exponential Poisson distribution revisited. Statistics: A Journal of Theoretical and Applied Statistics, 49:918–929.
Prieto, F. and Sarabia, J. M. (2017). A generalization of the power law distribution with nonlinear exponent. Communications in Nonlinear Science and Numerical Simulation, 42:215–228.
Prudente, A. A. and Cordeiro, G. M. (2010). Generalized Weibull linear models. Communications in Statistics - Theory and Methods, 39:3739–3755.
Raab, D. H. and Green, E. H. (1961). A cosine approximation to the Normal distribution. Psychometrika, 26:447–450.
Ramires, T. G., Ortega, E. M. M., M., C. G., and Hamedani, G. G. (2013). The Beta generalized half-Normal Geometric distribution. Studia Scientiarum Mathematicarum Hungarica, 50:523–554.
Ramos, M. W. A., Cordeiro, G. M., Marinho, P. R. D., Dias, C. R. B., and Hamedani, G. G. (2013a). The Zografos-Balakrishnan log-Logistic distribution: Properties and applications. Journal of Statistical Theory and Applications, 12:225–244.
Ramos, M. W. A., Marinho, P. R. D., and Cordeiro, G. M. (2015a). The Kumaraswamy-G Poisson family of distributions. Journal of Statistical Theory and Applications, 14:222– 239.
Ramos, M. W. A., Marinho, P. R. D., da Silva, R. V., and Cordeiro, G. M. (2013b). The exponentiated Lomax Poisson distribution with an application to lifetime data. Advances and Applications in Statistics, 34:107–135.
Ramos, M. W.A., Percontini, A., Cordeiro, G.M., and da Silva, R. V.(2015b). The Burr XII Negative Binomial distribution with applications to lifetime data. International Journal of Statistics and Probability, 4:109– 125.
Rasekhi, M., Afify, A. Z., and Yousof, H. M. (2016a). A new two parameter lifetime distribution with increasing, decreasing, bathtub and unimodal shapes for hazard rate. Personal Communication.
Rasekhi, M., Yousof, H. M., Alizadeh, M., Altun, E., and Hamedani, G. G. (2016b). The Topp-Leone generated Burr XII distribution: Bayesian analysis, characterizations and applications. Submitted.
Razaq, A. (2013). Some recent developments in the combinations of Gamma and Weibull distributions. PhD thesis, National College of Business Administration & Economics, Lahore, Pakistan.
Rezaei, S., Bahrami Sadr, B., Alizadeh, M., and Nadarajah, S. (2017). Topp-Leone generalized family of distributions: Properties and applications. Communications in Statistics - Theory and Methods, 46:2893–2909.
Ribereau, P., Masiello, E., and Naveau, P. (2016). Skew generalized extreme value distribution: Probability weighted moments estimation and application to block maxima procedure. Communications in Statistics - Theory and Methods, 45:5037–5052.
Ristić, M. M. and Kundu, D. (2016). Generalized exponential Geometric extreme distribution. Journal of Statistical Theory and Practice, 10:179–201.
Rodrigues, J. A., Silva, A. P. C. M., and Hamedani, G. G. (2015). The Beta exponentiated Lindley distribution. Journal of Statistical Theory and Applications, 14:60–75.
Saboor, A., Elbatal, I., and Cordeiro, G. M. (2017). The Transmuted exponentiated Weibull Geometric distribution: Theory and applications. Hacettepe Journal of Mathematics and Statistics, page To appear.
Saboor, A., Kamal, M., and Munir, A. (2015). The Transmuted Exponential-Weibull distribution with applications. Pakistan Journal of Statistics, 31:229–250.
Saboor, A. and Nadarajah, S. (2014). Corrigendum to ’some Gamma distributions’ by Saralees Nadarajah. Statistics: A Journal of Theoretical and Applied Statistics, 48:1185.
Saboor, A. and Pogány, T. (2016). Marshall-Olkin Gamma-Weibull distribution and applications. Communications in Statistics - Theory and Methods, 45:1550–1563.
Santos-Neto, M., Bourguignon, M., Zea, L. M., and Nascimento, A. D. C. (2014). The Marshall-Olkin extended Weibull family of distributions. Journal of Statistical Distributions and Applications, 1:1–24.
Sarhan, A. M. and Zaindin, M. (2009). Modified Weibull distribution. Applied Sciences, 11:123–136.
Shahrastani, S. Y., Shadrokh, A., and Yarmohammadi, M. (2016). The Beta-Weibull-logarithmic distribution. Journal of Iranian Statistical Society, 15:91–108.
Shakhatreh, M. K., Yusuf, A., and Mugdadi, A. R. (2016). The Beta generalized linear Exponential distribution. Statistics, 50:1346–1362.
Shakil, M. and Kibria, B. M. (2010). On a family of life distributions based on generalized Pearson differential equation with applications in health statistics. Journal of Statistical Theory and Applications, 9:255–281.
Shakil, M., Kibria, B. M. G., and Chang, K. C. (2007). Distributions of the product and ratio of Maxwell and Rayleigh random variables. Statistical Papers, 49:729–747.
Shakil, M., Kibria, B. M. G., and Singh, J. N. (2010a). A new family of distributions based on the generalized Pearson differential equation with some applications. Austrian Journal of Statistics, 39(3):259–278.
Shakil, M., Singh, J. N., and Kibria, B. M. (2010b). On a family of product distributions based on the Wittaker functions and generalized Pearson differential equation. Pakistan Journal of Statistics, 26:111–125.
Sharma, V. K., Singh, S. K., Singh, U., and Merovci, F. (2016). The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communications in Statistics - Theory and Methods, 45:5709–5729.
Silva, G. O., Ortega, E. M. M., Cancho, V. G., and Barreto, M. L. (2008). Log-Burr XII regression models with censored data. Computational Statistics and Data Analysis, 52:3820–3842.
Silva, G. O., Ortega, E. M. M., and Cordeiro, G. M. (2009). A log-extended Weibull regression model. Computational Statistics and Data Analysis, 53:4482–4489.
Tablada, C. J. and Cordeiro, G. M. (2017). The modified Fréchet distribution and its properties. Communications in Statistics - Theory and Methods, To appear.
Tahir, M., Alizadeh, M., Mansoor, M., Cordeiro, G. M., and Zubair, M. (2014a). The Weibull-power function distribution with applications. In Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics.
Tahir, M., Alzaatreh, A., Cordeiro, G. M., Zubair, M., and Mansoor, M. (2016a). The Weibull exponentiated-Exponential distribution with applications. Personal Communication.
Tahir, M., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., and Zubair, M. (2016b). The Weibull-Pareto distribution: Properties and applications. Communications in Statistics Simulation and Computation, 45:3548–3567.
Tahir, M., Cordeiro, G. M., Mansoor, M., and Zubair, M. (2015). Weibull-Lomax distribution: Properties and applications. Hacettepe Journal of Mathematics and Statistics, 44:455–474.
Tahir, M., Cordeiro, G. M., Mansoor, M., Zubair, M., and Alizadeh, M. (2016c). The Weibull-Dagum distribution: Properties and applications. Communications in Statistics - Theory and Methods, 45:7376–7398.
Tahir, M., Cordeiro, G. M., Mansoor, M., Zubair, M., and Alzaatreh, A. (2017a). The Kumaraswamy-Pareto IV distribution. Austrian Journal of Statistics, To appear.
Tahir, M., Zubair, M., Cordeiro, G. M., Alzaatreh, A., and Mansoor, M. (2017b). The Weibull-power Cauchy distribution: Model, properties and applications. Hacettepe Journal of Mathematics and Statistics, To appear.
Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., and Zubair, M. (2016d). The logistic-X family of distributions and its applications. Communications in Statistics Theory and Methods, 45:7326–7349.
Tahir, M. H., Mansoor, M., Zubair, M., and Hamedani, G. G. (2014b). McDonald log-Logistic distribution with an application to breast cancer data. Journal of Statistical Theory and Applications, 13:65–82.
Telcs, A., Glänzel, W., and Schubert, A. (1985). Characterization and statistical test using truncated expectations for a class of skew distributions. Mathematical Social Sciences, 10:169–178.
Vardhan, R. V. and Balaswamy, S. (2016). Transmuted new modified Weibull distribution. Mathematical Sciences and Applications E-Notes, 4:125–135.
Vianelli, S. (1982). Sulle curve lognormali di ordine r quali famiglie di distribuzioni di errori di proporzione. Statistica, 42:155–176.
Vianelli, S. (1983). The family of Normal and Lognormal distributions of order r. Metron, 41:3–10.
Ye, Y., Oluyede, B. O., and Pararai, M. (2012). Weighted generalized Beta distribution of the second kind and related distributions. Journal of Statistical and Econometric Methods, 1:13–31.
Yousof, H. M., Afify, A. Z., Alizadeh, M., Butt, N. S., Hamedani, G. G., and Ali, M. M. (2015). The Transmuted exponentiated generalized-G family of distributions. Pakistan Journal of Statistics and Operation Research, 11:441–464.
Yousof, H. M., Mahbubul Majumder, S. M. A., Jahanshahi, M., Masoom, A., and Hamedani, G. G. (2016). A new Weibull class of distributions. Submitted.
Zea, L. M., Silva, R. B., Bourguignon, M., Santo, A. M., and Cordeiro, G. M. (2012). The Beta exponentiated Pareto distribution with application to bladder cancer susceptibility. International Journal of Statistics and Probability, 2:8–19.
Zografos, K. and Balakrishnan, N. (2009). On families of Beta- and generalized Gamma-generated distributions and associated inference. Statistical Methodology, 6(4):344 – 362.

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