The Half-Logistic Lomax Distribution for Lifetime Modeling

Masood Anwar,Jawaria Zahoor

doi:10.1155/2018/3152807

Masood Anwar, Jawaria Zahoor

Open Access

https://doi.org/10.1155/2018/3152807

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Abstract

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

Highlights

The commonly used lifetime distributions have a limited range of behavior and do not provide adequate fit to complex data sets in different sciences
Motivated by the various applications of Lomax and half-logistic distributions in areas of income and wealth inequality, firm size, size of cities, queuing problems, actuarial science, medical and biological sciences, and engineering, we propose a two-parameter continuous lifetime distribution by compounding the halflogistic and the Lomax distribution called half-logistic Lomax (HLL) distribution
This paper aims to provide a new lifetime model with a minimum number of parameters by compounding the half-logistic and the Lomax distribution called half-logistic Lomax (HLL) distribution

Summary

Introduction

The commonly used lifetime distributions (exponential, gamma, Weibull, Lomax, lognormal, etc.) have a limited range of behavior and do not provide adequate fit to complex data sets in different sciences. Other models constitute flexible family of distributions in terms of the variates of shapes and hazard functions; see, for example, Al-Zahrani and Sagor [11], ElBassiouny et al [12], Rady et al [2], Kilany [13], and Tahir et al [3]. These generalizations of the Lomax distribution are considered to be useful life distribution models.

The HLL Distribution

Mathematical Properties

Estimation and Asymptotic Distribution

Simulation Study

Application

Concluding Remarks