TRANSMUTATION OF WEIBULL PARETO DISTRIBUTION

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TRANSMUTATION OF WEIBULL PARETO DISTRIBUTION

 

CHAPTER ONE

INTRODUCTION

1.1 Background to the study

In the field of Statistics and reliability engineering, the quality of the procedures used in statistical analysis depends heavily on the assumed probability distribution. Due to this fact, significant efforts have been made by many researchers in the development of standard probability distributions which are different from the known classical probability distribution. The standard probability distributions are obtained by generalizing the classical probability distribution such as exponential, Weibull, Pareto and Beta distributions. Application of probability distributions in engineering, medicine, finance, ICT among others, have further shown that many data sets do not follow the existing classical distributions. As a result of this, there is the need for development of standard probability distributions by generalization of some well-known classical distributions.

These distributions are derived by adding one or more parameters to the baseline model of continuous distributions. These families provide more flexibility in modelling and in analyzing real life data in many applied areas. For instance, the generalized transmuted-G family proposed by Nofalet al(2015), Transmuted Weibull Distribution: A Generalization of the Weibull Probability Distribution proposed by Aryal and Tsokos (2011), the transmuted geometric-G family introduced by Afifyet al(2016), the transmuted exponentiated generalized-G class of distributions defined by Yousofet al(2015), transmuted exponential distribution proposed by Enahoroet al(2015)and the Kumaraswamy transmuted-G family introduced by Afifyet al (2016).

Over the years, several attempts have been made to generalize the Weibull distribution by adding new parameters into the distribution which has led to the development of new distributions. For instance theExponentiated Weibull distribution (Pal et al 2003), Transmuted Weibull distribution (Gokarnal and Chris, 2011), Lomax-Weibul distribution (Almheidat et al 2015) ,Beta Weibull Distribution (Cordeiro et al 2012), New Weibull-Pareto distribution ( Suleiman and Albert 2015).These distributions have been found to be more flexible than the Weibull distribution when applied to real life data sets.

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TRANSMUTATION OF WEIBULL PARETO DISTRIBUTION