Estimating the parameter of an exponential distribution based on multiply progressive censored competing risks data

There are many situation in life testing experiments in which units are lost or removed from experimentation before failure. Therefore, multiply progressive censoring scheme was introduced. In lifetime data analysis, moreover, it is generally known that more than one cause or risk factor may be present at the same time. In this paper, therefore, we propose the estimators of the parameter and uncertainty measure of the exponential distribution under multiply progressive censored competing risk data. First, we derive the MLE for the parameter and uncertainty measure of exponential distribution. And we derive the Bayesian estimators for the parameter and uncertainty measure of exponential distribution under squared error loss function (SEL), precautionary loss function (PLF) and DeGroot loss function (DLF). We also compare the proposed estimators in the sense of the mean squared error (MSE) and bias under various multiply progressive censoring scheme. Finally, the validity of the proposed methods are demonstrated by a real data.