ODD GENERALIZED EXPONENTIAL-INVERSE-EXPONENTIAL DISTRIBUTION: IT’S PROPERTIES AND APPLICATIONS
CHAPTER ONE:
INTRODUCTION
1.1 Background of the Study
Statistical data modelling is an important aspect of statistics that attracts researcher’s wide attention. Modelling lifetime data in areas comprising reliability analysis, engineering, economics, biological studies, environmental and medical sciences, requires an appropriate statistical model for proper actualization of the data. However, there still remains problems where the real data does not follow any of the classical or standard probability models. To address this, there is strong need then to propose new models that can better capture real-life phenomenon inherent in a given dataset. Introducing new probability models or their classes is an old practice and has ever been considered as very valuable as many other practical problems in statistics.
The idea simply started with defining different mathematical functional forms, and then induction of location, scale or inequality parameters (Tahir and Cordeiro, 2016a). Addition of new shape parameter(s) expands a model into a larger family of distributions and can provides significantly skewed and heavy-tailed new distributions. It also provides greater flexibility in the form of new distributions. This induction of parameter(s) has been proved useful in exploring tail properties and also for improving the goodness-of-fit of the proposed generator family (Saboor et al., 2015).
The one parameter Inverse Exponential distribution otherwise known as the Inverted Exponential distribution was introduced by Keller and Kamath (1982). It has an inverted bathtub failure rate and it is a competitive model for the Exponential distribution. It is an important probability distribution for modelling lifetime data.
1.2 Statement of the Problem
There exist several probability distributions for modelling lifetime data.However, some of these dataset do not follow any of the existing and well known standard probability distributions or at least are inappropriately described by them. This brings increased interest in proposing new univariate continuous distributions by adding one or more new shape parameter(s) to the baseline model. In this dissertation, a new probability distribution called Odd Generalized Exponential-Inverse-Exponential distribution (OGE-IED) taking inverse-exponential as the baseline distribution and using Tahir et al., (2015) generator is being proposed, aimed to provide greater flexibility and create more weight to the tails of the new distribution.
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ODD GENERALIZED EXPONENTIAL-INVERSE-EXPONENTIAL DISTRIBUTION: IT’S PROPERTIES AND APPLICATIONS
