The Exponentiated Weibull-H Family of Distributions: Theory and Applications

A new class of continuous distributions called the exponentiated Weibull-H family is proposed and studied. The proposed class extends the Weibull-H family of probability distributions introduced by Bourguignon et al. (J Data Sci 12:53–68, 2014). Some special models of the new family are presented. Its basic mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating function, Rényi and Shannon entropies, order statistics, and probability weighted moments are derived. The maximum-likelihood method is adopted to estimate the model parameters and a simulation study is performed. The flexibility of the generated family is proved empirically by means of two applications to real data sets.

[1]  Francisco Louzada,et al.  An extended Lindley distribution , 2012 .

[2]  G. S. Mudholkar,et al.  Exponentiated Weibull family for analyzing bathtub failure-rate data , 1993 .

[3]  Pushpa L. Gupta,et al.  Modeling failure time data by lehman alternatives , 1998 .

[4]  Elisa Lee,et al.  Statistical Methods for Survival Data Analysis: Lee/Survival Data Analysis , 2003 .

[5]  Gauss M. Cordeiro,et al.  The Weibull-G Family of Probability Distributions , 2014, Journal of Data Science.

[6]  M. Mead.  A note on Kumaraswamy Fréchet distribution , 2014 .

[7]  G. G. Hamedani,et al.  The Burr X Generator of Distributions for Lifetime Data , 2017, J. Stat. Theory Appl..

[8]  W. J. Padgett,et al.  A Bootstrap Control Chart for Weibull Percentiles , 2006, Qual. Reliab. Eng. Int..

[9]  M. E. Ghitany,et al.  Power Lindley distribution and associated inference , 2013, Comput. Stat. Data Anal..

[10]  Elisa T. Lee,et al.  Statistical Methods for Survival Data Analysis , 1994, IEEE Transactions on Reliability.

[11]  M. H. Tahir,et al.  The odd generalized exponential family of distributions with applications , 2015 .

[12]  M. R. Mahmoud,et al.  On the Transmuted Frechet Distribution , 2013 .

[13]  G. G. Hamedani,et al.  The ExponentiatedWeibull-Pareto Distribution with Application , 2016, J. Stat. Theory Appl..

[14]  Samuel Kotz,et al.  The Exponentiated Type Distributions , 2006 .

[15]  Gauss M. Cordeiro,et al.  A New Lifetime Model: The Gamma Extended Fréchet Distribution , 2013, J. Stat. Theory Appl..

[16]  On the Exponentiated Generalized Modified Weibull Distribution , 2015 .

[17]  Erich L. Lehmann,et al.  The Power of Rank Tests , 1953 .

[18]  Gauss M. Cordeiro,et al.  The Exponentiated Generalized Class of Distributions , 2021, Journal of Data Science.