Συμβολή στη στατιστική συμπερασματολογία για τις κατανομές γάμα και αντίστροφη κανονική με χρήση της εμπειρικής ροπογεννήτριας συνάρτησης

Abstract

The subject of the present dissertation is the investigation of procedures of statistical inference for fitting and testing the gamma distribution and inverse Gaussian distribution, with data having positive skewness. These distributions are used widely in reliability analysis and lifetime models as well as in other applications. In the beginning, we describe alternative methods of statistical inference for the two and three-parameter families of gamma and inverse Gaussian distributions. Then, we examine methods of statistical inference in order to estimate the parameters of the two-parameter gamma distribution using the empirical moment generating function. Estimation procedures, like the method of mixed moments and the method of generalized least squares, are applied and compared with the method of maximum likelihood through Monte Carlo simulations. Also, we investigate goodness of fit tests for the two-parameter gamma distribution. These tests include the classical tests and a test based on the empirical moment generating function. Using Monte Carlo simulations, we compare the actual level of the tests and the power of the tests against skewed to the right distributions. We apply goodness of fit tests of gamma distributions to real life data, which have been examined earlier by other researchers. For the three-parameter gamma distribution we apply only one test using the empirical moment generating function since there are no classical tests using the empirical distribution function. Finally, we estimate quantiles of the inverse Gaussian distribution. We start estimating quantiles for the three-parameter distribution and then we apply two procedures which estimate quantiles for the two-parameter distribution. The estimates of the quantiles for each family of distributions use two procedures for estimating intermediary the parameters of the distribution. The procedures are compared with respect to the normalized mean square error and the relative bias using simulations.