Generalized Topp-Leone family of distributions
Abstract
Background & Aim: Adding parameters to an existing distribution to expand the family of distributions is a very common approach for developing more flexible models. Several ways for generating new distributions from classic ones have been developed.
Methods & Materials: A generalization of Topp-Leone generator of distributions was introduced. Several of its fundamental properties were obtained such as quantiles, moments, moment generating function (MGF), order statistics and maximum likelihood estimator (MLE).
Results: We provided four sub-models of the new family which extended some of the basic lifetime models such as exponential, Weibull, gamma and generalized exponential distributions. These distributions exhibited a wide range of shapes varying skewness and different forms of hazard rate function (HRF).
Conclusion: We have provided four new distributions. The flexibility of the proposed distributions and increased range of skewness were able to fit and capture features in one real dataset much better than some competitor distributions.
Eugene N, Lee C, Famoye F. Beta-normal distribution and its applications. Commun Stat Theory Methods 2002; 31(4): 497-512.
Alexander C, Cordeiro GM, Ortega EM, Sarabia JM. Generalized beta-generated distributions. Comput Stat Data Anal 2012; 56(6): 1880-97.
Zografos K, Balakrishnan N. On families of beta and generalized gamma-generated distributions and associated inference. Stat Methodol 2009; 6(4): 344-62.
Amini M, MirMostafaee SM, Ahmadi J. Log-gamma-generated families of distributions. Statistics A Journal of Theoretical and Applied Statistics 2014; 48(4): 913-32.
Ristic MM, Balakrishnan N. The gamma-exponentiated exponential distribution. J Stat Comput Simul 2012; 82(8): 1191-206.
Cordeiro GM, Ortega EM, da Cunha DC. The exponentiated generalized class of distributions. J Data Sci 2013; 11: 1-27.
Alzaatreh A, Lee C, Famoye F. A new method for generating families of continuous distributions. Metron 2013; 71(1): 63-79.
Alzaghal A, Famoye F, Lee C. Exponentiated "T"-"X" Family of Distributions with Some Applications. Int J Stat Probab 2013; 2(3):31-49.
Bourguignon M, Silva RB, Cordeiro GM. The weibull-g family of probability distributions. J Data Sci 2014; 12: 53-68.
Cordeiro GM, Alizadeh M, Ortega EM. The exponentiated half-logistic family of distributions: Properties and applications. J Probab Stat 2014; 2014: 864396.
Aljarrah MA, Lee C, Famoye F. On generating T-X family of distributions using quantile functions. J Stat Distrib Appl 2014; 1: 2.
Alzaatreh A, Lee C, Famoye F. T-normal family of distributions: A new approach to generalize the normal distribution. J Stat Distrib Appl 2014; 1: 16.
Cordeiro GM, Ortega EMM, Popovi-ē BV, Pescim RR. The Lomax generator of distributions: Properties, minification process and regression model. Appl Math Comput 2014; 247(Supplement C): 465-86.
Cordeiro GM, Ortega EM, Silva GO. The Kumaraswamy modified Weibull distribution: Theory and applications. J Stat Comput Simul 2014; 84(7): 1387-411.
Alizadeh M, Doostparast M, Emadi M, Cordeiro GM, Ortega EM, Pescim RR. A new family of distributions: The Kumaraswamy odd log-logistic, properties and applications. Hacettepe J Math Stat 2015; 44(6): 1491-512.
Tahir MH, Cordeiro GM, Alzaatreh A, Mansoor M, Zubair M. The logistic-X family of distributions and its applications. Commun Stat Theory Methods 2016; 45(24): 7326-49.
Mahdavi A, Kundu D. A new method for generating distributions with an application to exponential distribution. Commun Stat Simul Comput 2017; 46(13): 65576543.
Al-Shomrani A, Arif O, Shawky A, Hanif S, Shahbaz MQ. Topp-Leone Family of Distributions: Some Properties and Application. Pak J Stat Oper Res 2016; 12(3): 443-51.
Greenwood JA, Landwehr JM, Matalas NC, Wallis JR. Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form. Water Resour Res 1979; 15(5): 1049-54.
Gupta RD, Kundu D. Theory & Methods:Generalized exponential distributions. Aust N Z J Stat 1999; 41(2): 173-88.
Bjerkedal T. Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. Am J Hyg 1960; 72: 130-48.
Gupta RD, Kundu D. A new class of weighted exponential distributions. Statistics 2009; 43(6): 621-34.
Kharazmi O, Mahdavi A, Fathizadeh M. Generalized weighted exponential distribution. Commun Stat Simul Comput 2015; 44(6): 1557-69.
Sangsanit Y, Bodhisuwan W. The Topp-Leone generator of distributions: Properties and inferences. Songklanakarin J Sci Technol 2016; 38(5): 537-48.
Rezaei S, Bahrami Sadr B, Alizadeh M, Nadarajah S. Topp-Leone generated family of distributions: Properties and applications. Commun Stat Theory Methods 2017; 46(6): 2893-909.
R Development Core Team. R: A language and environment for statistical computing. Vienna, Austria: The R Foundation for Statistical Computing; 2011.
| Files | ||
| Issue | Vol 3 No 2 (2017) | |
| Section | Original Article(s) | |
| Keywords | ||
| Statistical distributions Likelihood functions Survival analysis | ||
| Rights and permissions | |
|
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
