Marshall–Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics

Hisham Mohamed Almongy,Ehab Mohamed Almetwally,Amaal Elsayed Mubarak

doi:10.18187/pjsor.v17i1.3402

Hisham Mohamed Almongy, Ehab Mohamed Almetwally + Show 1 more

Open Access

https://doi.org/10.18187/pjsor.v17i1.3402

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Abstract

In this paper, we introduce and study a new extension of Lomax distribution with four-parameter named as the Marshall–Olkin alpha power Lomax (MOAPL) distribution. Some statistical properties of this distribution are discussed. Maximum likelihood estimation (MLE), maximum product spacing (MPS) and least Square (LS) method for the MOAPL distribution parameters are discussed. A numerical study using real data analysis and Monte-Carlo simulation are performed to compare between different methods of estimation. Superiority of the new model over some well-known distributions are illustrated by physics and economics real data sets. The MOAPL model can produce better fits than some well-known distributions as Marshall–Olkin Lomax, alpha power Lomax, Lomax distribution, Marshall–Olkin alpha power exponential, Kumaraswamy-generalized Lomax, exponentiated Lomax and power Lomax.

Highlights

The Lomax distribution has been introduced by Lomax (1954)
We propose a new four-parameter model, called the Marshall-Olkin alpha power Lomax (MOAPL) distribution, which is a new extension of the Lomax distribution
The Marshall–Olkin alpha power Lomax (MOAPL) distribution is motivated by the wide utilization of the Lomax model in life testing and provides more flexibility to analyze lifetime data

Summary

Introduction

The Lomax distribution has been introduced by Lomax (1954). The probability distribution of Lomax is a heavy-tail and often used in business, economics, and actuarial modeling. Many authors have discussed more applications by using Lomax distribution. See Chahkandi and Ganjali (2009), Hassan and Al-Ghamdi (2009), Abd-Elfattah and Alharbey (2010), Ashour et al (2011), Nasiri and Hosseini (2012), Helu et al (2015), Hassan et al (2016) and El-Sherpieny et al (2020), all of them used Lomax distribution for different applications. The CDF and pdf of Lomax distribution with parameters β and λ are given respectively, as x −β

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