Point Estimation of Three Parameter Crack Distribution
Date
2015-03
Authors
Das, Suporna
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Graduate Studies and Research, University of Regina
Abstract
The three parameter Crack distribution is a mixture of the two parameter Inverse
Gaussian distribution and Length Biased Inverse Gaussian distribution and
Birnbaum-Saunders distribution is a special case for p = 1
2 ; where 0 p 1, is
the weight parameter. In this thesis, we have developed and investigated estimation
method and procedures in order to estimate parameters of the Crack distribution.
First we focused on the derivation of the Moment Generating Function to construct
a new method in order to find the first four raw moments, which are used to estimate
parameters by Method of Moments. For illustration purpose we considered four real
data sets, which indicated the goodness of fit and flexibility of the Crack model. In
addition, we proposed composition method to generate Crack random number and
developed algorithm and estimation procedure to estimate parameters in order to
calibrate Bias, Variance and Mean Square Error. Results of the simulation are presented
numerically and graphically for various scenarios to compare the performance
of the Method of Moments and Maximum Likelihood Estimates. The shape of the
Crack density functions are also illustrated graphically for some specific values of
parameters. The simulated and real data are studied by using Excel and Matlab.
Description
A Thesis Submitted to the Faculty of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Statistics, University of Regina. xxviii, 146 p.