Topp–Leone generated family of distributions: Properties and applications

ABSTRACT We introduce a new family of distributions based on a one-parameter distribution exhibiting bathtub-shaped hazard rates. We study the mathematical properties of the family and estimate its parameters by the method of maximum likelihood. Finally, the usefulness of the family is illustrated using a real dataset.

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

[2]  Ali I. Genç.  Estimation of P(X>Y) with Topp–Leone distribution , 2013 .

[3]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[4]  S. Kotz,et al.  Two-sided generalized Topp and Leone (TS-GTL) distributions , 2008 .

[5]  Ali I. Genç.  Moments of order statistics of Topp–Leone distribution , 2012 .

[6]  M. Aslam,et al.  Bayesian Estimation for Topp-Leone Distribution under Trimmed Samples , 2013 .

[7]  Jurgen A. Doornik,et al.  Ox: an Object-oriented Matrix Programming Language , 1996 .

[8]  T. Ferguson.  A Course in Large Sample Theory , 1996 .

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

[10]  J. Ahmadi,et al.  Log-gamma-generated families of distributions , 2014 .

[11]  David J. Lunn,et al.  Survival extrapolation using the poly-Weibull model , 2015, Statistical methods in medical research.

[12]  Dipak K. Dey,et al.  Bayesian modeling of bathtub shaped hazard rate using various Weibull extensions and related issues of model selection , 2012, Sankhya B.

[13]  H. Müller,et al.  Hazard rate estimation under random censoring with varying kernels and bandwidths. , 1994, Biometrics.

[14]  Saralees Nadarajah,et al.  The Kumaraswamy Gumbel distribution , 2012, Stat. Methods Appl..

[15]  Samuel Kotz,et al.  On some reliability measures and their stochastic orderings for the Topp–Leone distribution , 2005 .

[16]  Ingram Olkin,et al.  Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families , 2007 .

[17]  Saralees Nadarajah,et al.  A new lifetime distribution , 2014 .

[18]  Eric R. Ziegel,et al.  Data: A Collection of Problems From Many Fields for the Student and Research Worker , 1987 .

[19]  Fred C. Leone,et al.  A Family of J-Shaped Frequency Functions , 1955 .

[20]  S. Kotz,et al.  Kurtosis of the Topp-Leone distributions , 2022 .

[21]  Record values from a family of J-shaped distributions , 2011 .

[22]  Samuel Kotz,et al.  Moments of some J-shaped distributions , 2003 .

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