Abstract
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.
Highlights
The nth incomplete moment of a distribution play an important role in applications
Order statistics have been extensively applied in many fields of statistics, such as reliability and life testing
A numerical evaluation is carried out to examine the performance of maximum likelihood estimators for TIIGTLE model
Summary
The Topp-Leone (TL) distribution was originally proposed by Topp and Leone (1955) as an alternative to beta distribution and it has been applied for some failure data It is a one-parameter distribution with cumulative distribution function (cdf) and the probability density function (pdf) specified by. Ristic and Balakrishnan (2012) proposed a gamma generator for any continuous distribution G(x) with the following cdf. Our objective here, is to introduce a new generated family of continuous distributions with two extra shape parameters based on cdf (3) by taking Topp-Leone distribution as a generator and the upper bound to be 1 G (x ; ). We call the new generated family as Type II generalized Topp–Leone which has the cdf specified by.
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