A New Approach to Probability Distributions

Abstract

Statistics is concerned with making inferences about the way the world is based upon things we observe happening. Statistical distributions are commonly applied to describe real world phenomena. Due to the usefulness of statistical distributions, this theory is widely studied and new distributions are developed. The interest in developing more flexible statistical distributions remains strong in statistical profession. For any continuous baseline F distribution newlineShaw et al. (2007) proposed Transmuted generated F-family of distributions using Quadratic transmutation. Lee and Famaye (2014) proposed the T-X family of distributions. As part of these newlinetwo families, we proposed three models Transmuted Inverse Rayleigh, Transmuted Generalized newlineInverse Exponential and Weibull-Rayleigh distribution. Applications are also stated as to why these distributions have studied and some structural properties of these distributions have also studied. This thesis is divided in to six chapters; chapter wise summary is given below: newlineChapter One: This chapter is introductory in nature and provides genesis of the probability distributions. Definitions and pre-requisites and other preliminaries are also presented in this chapter. An extensive brief survey of the literature available on the topic has been reviewed. newlineChapter Two: In this chapter, we have introduced a new model called Transmuted Generalized Inverse exponential distribution. The structural and characterizing properties including moments, moment generating function, entropy, reliability and hazard function etc have been studied and derived. The estimation of parameters of new model has been obtained by employing maximum newlinelikelihood estimation (both censored and uncensored cases). newlineChapter Three: In this chapter, our objective is to study the Bayes estimates of the shape parameter of Exponentiated-Exponential distribution. The prior distribution used is the extended newlineJeffrey s prior and three informative priors viz Chi-Square prior, Pareto 1 prior and inverse Levy newlineprior.......