# EXPONENTIATED-EXPONENTIAL WEIBULL DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS

0
43

### EXPONENTIATED-EXPONENTIAL WEIBULL DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS

CHAPTER ONE

INTRODUCTION

1.1    Background to the Study

Several classical distributions have been widely used over the past decades for mod-elling lifetime data in many areas such as reliability, engineering, economics, biolog-ical studies, environmental actuarial, environmental and medical sciences, demog-raphy, and insurance. However, in many applied areas such as lifetime analysis, finance, and insurance, there is a clear need for extended forms of these distribu-tions. This is because there still remain many important problems where the real data does not follow any of the classical or standard probability models. For that reason, numerous methods for generating new families of distributions have been considered (Bourguignon et al., 2014). To handle this, there is a strong need to propose useful models for the better study of the real-life marvel. Introducing new probability models or their classes is an old practice and has ever been considered as valuable as many other practical problems in statistics. According to Tahir and Cordeiro (2016), the idea simply started with defining diﬀerent mathematical func-tional forms, and then adding of location, scale or shape parameter(s).

Inducing of a new shape parameter(s) introduces a model into greater family of distributions and can give significantly skewed and heavy-tailed distributions and also provides greater flexibility in the form of new distribution. Gupta et al., (1998) proposed a generator for defining a new univariate continuous family of distribu-tions by adding one shape parameter to the baseline (parent) distribution. Gupta and Kundu (1999) pioneered the study of two-parameter generalization, in which they studied two-parameter Generalized-Exponential (GE) distribution also called Exponentiated-Exponential (EE) distribution, after which several other authors worked on GE distribution due to its attractive features, among which are Gupta and Kundu (2001a, 2001b, 2002 and 2003), Kundu et al., (2005) among others.

The authors present two real life data sets, where it is observed that in one data set Ex-ponentiated exponential distribution has a better fit compared to Weibull or gamma distribution and in the other data set Weibull has a better fit than Exponentiated exponential or gamma distribution. The induction of parameter(s) has been proved useful in discovering tail properties and also for improving the goodness-of-fit of the proposed distribution (Saboor et al., 2015).