Laplace distribution and its generalizations

Abstract

In this project construction of Laplace distribution has been reviewed using the difference method,method of mixture,product of Rayleigh and normal distributions.The properties of Laplace distribution including mgf,skewness and kurtosis have been determined. A generalization of Laplace distribution has been studied based on Beta generated distribution, generalized Laplace distribution,Laplace mixtures and Exponential power mixtures. Both Laplace mixtures and Exponential power mixtures are obtained using 16 mixing distributions through the methods of modified Bessel function of the third kind and in terms of confluent hypergeometric function.The the rth moments for Laplace mixtures are looked into.In addition, the classical cases of EP when r = 1 giving rise to Laplace distribution and when r = 2 to yield normal distribution are also studied.