Int. J. Agricult. Stat. Sci., Vol. 7, No. 1, pp. 15-29, 2011
ISSN : 0973-1903
RELIABILITY ESTIMATION IN GENERALIZED GAMMA DISTRIBUTION WITH PROGRESSIVELY CENSORED DATA Hare Krishna* and Kapil Kumar Department of Statistics, C. C. S. University, Meerut – 250 004, India. E-mail :
[email protected]
Abstract Generalized gamma distribution is a generalization of most of the life time models, such as Exponential, Gamma, Weibull, Rayleigh, Pareto, Extreme Value, Half-Normal and Lognormal. With a progressive type II right censored sample, we drive in this article, the maximum likelihood and Bayes estimates of the scale parameter of generalized gamma distribution. Asymptotic results based on the maximum likelihood estimate, interval estimation and coverage probability of the parameter are considered. A Monte Carlo simulation study is performed to compare these estimates. Also, a real data example is considered for the purpose of illustration. Key words : Generalized gamma distribution, Progressive censored data, Coverage probability.
1. Introduction In reliability theory, the lifetime behavior of a system is characterized by lifetime distributions. There are several parametric lifetime distributions used in the analysis of the life testing experiments. Some of the most popular lifetime distributions are Exponential, Gamma, Weibull, Rayleigh, Pareto, Extreme Value, Half-Normal and Lognormal. [Lawless (2003)]. The generalized gamma distribution was first proposed by Stacy (1962). It was proposed independently by Cohen (1969) as a generalized weibull distribution. This distribution has also been considered by Harter (1967). These authors have developed estimation procedures for generalized gamma distribution with complete samples. Sometimes testing facilities are available only for a fixed time period, so, to complete the experiment within time, the experiment is designed so that a number of items are removed either at prefixed time points or at failure of prefixed number of items. When n items are put on test and only m (m ≤ n) are actually observed to fail, it is called censoring. There are many types of censoring schemes. In this paper, we consider progressive Type II right censoring, which includes the conventional Type II right censoring as a particular case. Suppose n identical items are put on a life testing experiment and the progressive censoring scheme R~ = R1 , R2 , ...., Rm is pre-fixed such that after the first failure R1 surviving items
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*Author for correspondence.
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