New Weighted Lomax (NWL) Distribution with Applications to Real and Simulated Data

Ishfaq Ahmad,Huda M. Alshanbari,Abd Al-Aziz Hosni El-Bagoury,Javid Gani Dar,Muhammad Ijaz,Syed Muhammad Asim

doi:10.1155/2021/8558118

Abstract

The rationale of the paper is to present a new probability distribution that can model both the monotonic and nonmonotonic hazard rate shapes and to increase their flexibility among other probability distributions available in the literature. The proposed probability distribution is called the New Weighted Lomax (NWL) distribution. Various statistical properties have been studied including with the estimation of the unknown parameters. To achieve the basic objectives, applications of NWL are presented by means of two real-life data sets as well as a simulated data. It is verified that NWL performs well in both monotonic and nonmonotonic hazard rate function than the Lomax (L), Power Lomax (PL), Exponential Lomax (EL), and Weibull Lomax (WL) distribution.

Highlights

From the last few years, it is usual practice to make a contribution to the existing theory of probability due to its wide application in different fields of sciences, for example, in reliability analysis, signal processing, survival analysis, and so on
Lemonte et al [1] introduced the additive Weibull distribution by adding the two Weibull distributions, Al-Aqtash et al [2] presented the new family of distribution with a logit function, Aldeni et al [3, 4] explored by employing the quantile function, Alzaatreh et al investigated the gamma-normal distribution [5], and references [6,7,8,9,10,11] presented new probability distributions using transmutation technique
To increase the flexibility of the model, modification of this distribution has been done by many researchers; for example, Ashour and Eltehiwy [10] introduced transmuted Lomax distribution, Ashour and Eltehiwy [11] transmuted Exponentiated Lomax distribution, Lemonte and Cordeiro [13] explored the extended Lomax, Cordeiro et al [14] defined gamma-Lomax, Ghitany et al [15] presented Marshall–Olkin extended Lomax and discussed their applications to censored data, Al-Zahrani and Sagor [16] modified Poisson Lomax distribution

Summary

Introduction

From the last few years, it is usual practice to make a contribution to the existing theory of probability due to its wide application in different fields of sciences, for example, in reliability analysis, signal processing, survival analysis, and so on. To increase the flexibility of the model, modification of this distribution has been done by many researchers; for example, Ashour and Eltehiwy [10] introduced transmuted Lomax distribution, Ashour and Eltehiwy [11] transmuted Exponentiated Lomax distribution, Lemonte and Cordeiro [13] explored the extended Lomax, Cordeiro et al [14] defined gamma-Lomax, Ghitany et al [15] presented Marshall–Olkin extended Lomax and discussed their applications to censored data, Al-Zahrani and Sagor [16] modified Poisson Lomax distribution. Considering a continuous random variable Y, the CDF of a New Weighted Lomax distribution is defined by β ey − α.

Parameter Estimation

Stress Strength Parameter

10. Rank Regression on Y

12. Applications