Inferences Based on Correlated Randomly Censored Gumbel’s Type-I Bivariate Exponential Distribution

The formal random censoring plan has been extensively studied earlier in statistical literature by numerous researchers to deal with dropouts or unintentional random removals in life-testing experiments. All of them considered failure time and censoring time to be independent. But there are several situations in which one observes that as the failure time of an item increases, the censoring time decreases. In medical studies or especially in clinical trials, the occurrence of dropouts or unintentional removals is frequently observed in such a way that as the treatment (failure) time increases, the dropout (censoring) time decreases. No work has yet been found that deals with such correlated failure and censoring times. Therefore, in this article, we assume that the failure time is negatively correlated with censoring time, and they follow Gumbel’s type-I bivariate exponential distribution. We compute the maximum likelihood estimates of the model parameters. Using the Monte Carlo Markov chain methods, the Bayesian estimators of the parameters are calculated. The expected experimental time is also evaluated. Finally, for illustrative purposes, a numerical study and a real data set analysis are given.