Type II Generalized Topp–Leone Family of Distributions: Properties and Applications

Journal of Data Science

article

Amal S. Hassan¹  M. Elgarhy²  Zubair Ahmad³ 

[1] Faculty of Graduate Studies for Statistical Research ,(FGSSR), Cairo University, Department of Mathematical Statistics;Valley High Institute for Management Finance and Information Systems;Department of Statistics, Quaid-i-Azam University

关键词: Topp–Leone distribution;    Order statistics;    Rényi entropy;   

DOI  :  10.6339/JDS.201910_17(4).0001

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

The Topp-Leone distribution is an attractive model for life testing and reliability studies as it acquires a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp–Leone random variable as a generator, called the Type II generalized Topp– Leone–G (TIIGTL-G) family. Its density function can be unimodel, leftskewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down, J and reversed-J hazard rates. Some special models are presented. Some of its statistical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp–Leone exponential is illustrated through two real data sets.

【 授权许可】

CC BY