Estimating the Parameter of a Exponential Distribution under Multiply Type II Censored Competing Risks Data

Abstract

In lifetime data analysis, it is generally note that more than 1 risk factor (RF) may be appear at the same moment. Namely, a failure of unit is often arisen by one of the RFs. Moreover, it is known that the lifetimes of items may not be checked exactly. Therefore, we derive the estimators of parameters of exponential distribution (ED) with multiply type II censored competing risks (MCCR) data. We consider the maximum likelihood estimator (MLE) for parameters of ED with MCCR data. We also obtain the Bayes estimators (BEs) for parameter of the ED with MCCR data under the squared error loss function (SELF), DeGroot loss function (DLF) and precautionary loss function (PLF). Lindley’s approximate (LA) method is used to compute these BEs. The BEs of parameters are better than the respective MLE in terms of mean squared errors (MSEs) and biases. The choice of SELF seems to be a reasonable choice for Bayes estimation of parameters. A real data analysis has been provided.