ESTIMATION OF THE PARAMETERS AND RELIABILITY OF THE INVERSE GAUSSIAN DISTRIBUTION BASED ON CENSORED SAMPLES

Abstract

The inverse Gaussian distribution is very relevant for studying reliability and life-testing problems. Its definition as being the first passage time distribution for the wiener process makes it particularly appropriate for failure or reaction time data analysis.

The objective of this study is to estimate the parameters and the reliability function of the three parameters inverse Gaussian distribution and of a mixture of two inverse Gaussian distributions.

In the Bayesian approach, a squared error loss function is usually used. The resulting estimate of any function of the parameters is the posterior expectation of that function. This expectation is always given as a ratio of two integrals which in many cases can not be found in a compact form.

In this thesis we apply an approximation proposed by Lindley (1980) which can be used easily to find the posterior expectation in a simple way with no need to numerical integration