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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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