# A STUDY ON THE PROPERTIES AND APPLICATIONS OF LOMAX-GOMPERTZ DISTRIBUTION

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ABSTRACT

The Gompertz distribution can be skewed to the right or to the left. This dissertation introduces a

new positively skewed Gompertz model known as Lomax-Gompertz Distribution (LGD). This

extension was possible with the aid of a Lomax generator.Some basic statistical propertiesof the

new distribution such as moments, moment generating function, characteristics function, reliability

analysis, quantile function and distribution of order statistics were derived. A plot of the probability

density function (pdf)of the distribution revealed that it ispositively skewed. The model parameters

have been estimated using the method of maximum likelihood estimation.The plot for the survival

function indicates that the Lomax-GompertzDistribution could be used to model time or age-

dependent variables, where probability of survival decreases with time or age.The performance of

the Lomax-GompertzDistribution has been compared to the Generalized Gompertz, Transmuted

Gompertz, Odd Generalized Exponential Gompertz and the Gompertz distributions by some

applications to three real-life data sets. The results show that the proposed distribution

outperformed the Generalized Gompertz, Transmuted Gompertz, Odd Generalized Exponential

Gompertz and the Gompertz distributions in two of the datasets. The model should be used to

modelpositively skewed datasets with various peaks where the sample size is large.

CHAPTER ONE

BACKGROUND TO THE STUDY

1.1 Introduction

Lomax (1954) pioneered the study of a distribution used for modeling business failure data

called the Lomax or Pareto II distribution. This distribution has found wide application in a

variety of fields such as income and wealth inequality, size of cities, actuarial science, medical

and biological sciences, engineering, lifetime and reliability modeling. It has been applied to

model data obtained from income and wealth (Harris, 1968), firm size (Corbellini et al., 2007),

size distribution of computer files on servers (Holland et al.,1989), reliability and life testing

(Hassan and Al-Ghamdi, 2009), receiver operating ch

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