Abstract
This paper introduces a new four-parameter lifetime model called the Topp Leone Generated Weibull (TLGW) distribution. This distribution is a generalization of the two parameter Weibull distribution using the genesis of Topp-Leone distribution. We derive many of its structural properties including ordinary and incomplete moments, quantile and generating functions and order statistics. Parameter estimation using maximum likelihood method and simulation results to assess effectiveness of the distribution are discussed. Also, for the first time, we introduce a regression model based on the new distribution. We prove empirically the importance and flexibility of the new model in modeling various types of real data sets.
Highlights
The Weibull distribution has an undeniable popularity in probability and statistics due to its versatility of modeling real world data
In this paper we introduce a new generalization of the Weibull distribution using the genesis of the Topp-Leone distribution and is named as Topp-Leone Generated Weibull (TLGW) distribution
We propose a new four parameter model, called the Topp-Leone Generated Weibull (TLGW) distribution, which extends the Weibull distribution
Summary
The Weibull distribution has an undeniable popularity in probability and statistics due to its versatility of modeling real world data. It has been proven that several of these generalized distribution are more flexible and are capable of modeling real world data better than the classical Weibull distribution. In this paper we will use this generalization to the Weibull (W) distribution whose pdf and cdf are given, respectively, by g(x) = βηβ xβ−1 e−(ηx)β (3). In order to derive mathematical and statistical properties of the TLGW distribution, the series expansion of its pdf and cdf will be useful. Weibull (exp-W) distribution with power parameter γ This means the TLGW distribution can be expressed as a linear mixture of the exp-W distribution.
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