Extended Odd Fréchet-G Family of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

[1]  F. Famoye,et al.  Exponentiated $T$-$X$ Family of Distributions with Some Applications , 2013 .

[2]  Gauss M. Cordeiro,et al.  A new family of generalized distributions , 2011 .

[3]  H. Akaike.  A new look at the statistical model identification , 1974 .

[4]  Sam C. Saunders,et al.  ESTIMATION FOR A FAMILY OF LIFE DISTRIBUTIONS WITH APPLICATIONS TO FATIGUE , 1969 .

[5]  Sam C. Saunders,et al.  Estimation for a family of life distributions with applications to fatigue , 1969, Journal of Applied Probability.

[6]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[7]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[8]  B. Bolker.  Tools for General Maximum Likelihood Estimation [R package bbmle version 1.0.23.1] , 2020 .

[9]  Konstantinos Adamidis,et al.  A Family of Lifetime Distributions , 2012 .

[10]  G. Crooks.  On Measures of Entropy and Information , 2015 .

[11]  Analysing Activities in a Classroom - Remembrances of Professor John Aitchison in Hong Kong with Applications to a Service Provider , 2018, Austrian Journal of Statistics.

[12]  M. Elgarhy,et al.  The Odd Frѐchet-G Family of Probability Distributions , 2018 .

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

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

[15]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[16]  G. Cordeiro,et al.  The Beta Extended Weibull Family , 2009 .

[17]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[18]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[19]  G. Cordeiro,et al.  The Topp–Leone odd log-logistic family of distributions , 2017 .

[20]  M. H. Tahir,et al.  Odd Burr-G Poisson Family of Distributions , 2018 .

[21]  Oscar Ngesa,et al.  Exponentiated Generalized Transformed-Transformer Family of Distributions , 2017 .

[22]  Debasis Kundu,et al.  A new method for generating distributions with an application to exponential distribution , 2017 .

[23]  Kahadawala Cooray,et al.  Generalization of the Weibull distribution: the odd Weibull family , 2006 .

[24]  Gauss M. Cordeiro,et al.  The Odd Lindley-G Family of Distributions , 2017 .

[25]  The Generalized Odd Gamma-G Family of Distributions: Properties and Applications , 2018 .

[26]  Ayman Alzaatreh,et al.  A new method for generating families of continuous distributions , 2013 .