Abstract
Gamma and log-logistic distributions are two popular distributions for analyzing lifetime data. In this paper, the problem of discriminating between these two distribution functions is considered in case of progressive type II censoring. The ratio of the maximized likelihood test (RML) is used to discriminate between them. Some simulation experiments were performed to see how the probability of correct selection (PCS) under each model work for small sample sizes. Real data life is analyzed to see how the proposed method works in practice. As a special case of progressive type II censoring, the problem of discriminating between gamma and log-logistic in case of complete samples is considered. The RML and the ratio of Minimized Kullback-Leibler Divergence (RMKLD) tests are used to discriminate between them. The asymptotic results are used to estimate the PCS which is used to calculate the minimum sample size required for discriminating between two distributions. Two real life data are analyzed.
Highlights
Choosing the correct or best-fitting distribution for a given data set is an important issue
The probability of correct selection (PCS) for ratio of Minimized Kullback-Leibler Divergence (RMKLD) is 83% and 77% for ratio of the maximized likelihood (RML) which indicates the error type I equals to 17% for RMKLD and 23% for RML. consider in table 10 the case σ= 2.2 The PCS for RMKLD is 57% and 51% for RML which indicates the error type I equals to 43% for RMKLD and 49% for RML It found that both methods behave for example, as sample size increases the PCS capture higher values, as expected
The problem of discriminating gamma and log-logistic is considered in case of progressive type II censoring
Summary
Choosing the correct or best-fitting distribution for a given data set is an important issue. Atkinson (1970) combined Cox's two hypotheses in a general model and applied his test to discriminate between lognormal and exponential distribution. The conventional Type-I and Type-II censoring schemes do not have the flexibility of allowing removal of units at points other than the terminal point of the experiment. Because of this lack of flexibility, a more general censoring scheme called progressive Type-II right censoring has been introduced.
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