Abstract
In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.
Highlights
For several decades, researchers have been working to come up with several new distributions to meet certain practical requirements
The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered
This issue is addressed in this work by making the use of the shape parameter and it is performed in the proposed KPL distribution
Summary
Researchers have been working to come up with several new distributions to meet certain practical requirements. If a = b = 1, the forms in (3) and (4) reduce to the pdf and cdf from the base distribution This generalized version of the Kw distribution is called the Kw-G family of distributions. The goal of providing new distributions is to create flexible mathematical models capable of handling non-normal data scenarios This flexibility can be achieved in a simple way by adding additional parameters such as location, scale and shape. Mentioned that the hazard rate function (hrf) of the PL distribution does not have an increasing curve, which remains a serious limitation for some modeling purposes This issue is addressed in this work by making the use of the shape parameter and it is performed in the proposed KPL distribution.
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