A Generalization of the Moyal Distribution

Abstract

In this thesis, a three parameter generalization of Moyal distribution and also a four parameter generalization of Moyal distribution are obtained, with the purpose of obtaining a more flexible model relative to the behaviour of hazard rate functions. Various statistical properties such as density, hazard rate functions, quantile function, mode, moments, incomplete moments, moment generating functions, mean deviation, Lorenz, Bonferroni and Zenga curves, Renyi and continuous entropies and distribution of r^th order statistics have been derived. The method of maximum likelihood estimation has been used to estimate the parameters of the generalized Moyal distributions and the observed information matrix is derived. Further confidence intervals are also obtained. Finally applicability of the proposed models to the real data is analyzed. A comparison has also been made with some existing distributions.