Probability models associated with Kratzel function and their applications

Abstract

The main objective of statistical distribution theory is to investigate the properties of random phenomena. Random phenomenon is a non-deterministic situation of the physical or experimental process. Many statistical models are available in the literature for modeling various areas of non-deterministic situations. But in some situations, classical distributions like normal, gamma, Weibull, Poisson etc may not be flexible enough for describing the statistical behavior of the data. For handling such situations, several statistical methods have been used to generate the statistical models which include methods of mixing or compounding, method of transformation of variables, Bayesian procedure etc. The present thesis titled Probability Models Associated with Kr¨ atzel Function and their Applications is concerned mainly with statistical models based on the concept of compound (mixture) distributions. This work is devoted to construct some generalized compound models with the help of special functions and their applications in SAR images, composite fading channels etc. The motivation behind this work is the applicability of special functions in a number fields such as statistical distribution theory, theoretical physics, communication and engineering, fractional differential and integral equations etc. The whole thesis is divided into 5 chapters.