Exact likelihood-based point and interval estimation for Laplace distribution based on Type-II right censored samples

In this paper, we first present explicit expressions for the maximum likelihood estimators (MLEs) of the location and scale parameters of the Laplace distribution based on a Type-II right censored sample under different cases. Next, we derive the joint moment generating function of the MLEs of the two parameters and use it to obtain the bias and mean squared error of the MLEs for all the cases. We then derive the exact density functions of the MLEs and utilize them to develop exact confidence intervals for the parameters. 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.