Exact predictive likelihood inference for Laplace distribution based on a time-constrained experiment

In this paper, we will first derive explicit expressions for the predictive maximum likelihood estimators (PMLEs) for Laplace distribution based on a time-constrained life-testing experiment. Next, we derive the exact conditional distribution of the likelihood predictor of the s-th failure through the use of exact conditional moment generating function (MGF). We develop three different exact prediction intervals for the future failure, and a Monte Carlo simulation study is then carried out to check the accuracy of the derived exact inference. Finally, an example is presented to illustrate all the inferential results developed here.