Exact Likelihood-Based Point and Interval Estimation for Lifetime Characteristics of Laplace Distribution Based on a Time-Constrained Life-Testing Experiment

In this paper, we first derive explicit expressions for the MLEs of the location and scale parameters of the Laplace distribution based on a Type-I right-censored sample arising from a time-constrained life-testing experiment by considering different cases. We derive the conditional joint MGF of these MLEs and use them to derive the bias and MSEs of the MLEs for all the cases. We then derive the exact conditional marginal and joint density functions of the MLEs and utilize them to develop exact conditional CIs for the parameters. We also briefly discuss the MLEs of reliability and cumulative hazard functions and the construction of exact CIs for these functions. Next, a Monte Carlo simulation study is carried out to evaluate the performance of the developed inferential results. Finally, some examples are presented to illustrate the point and interval estimation methods developed here under a time-constrained life-testing experiment.