Exact Likelihood-Based Point and Interval Estimation for Lifetime Characteristics of Laplace Distribution Based on hybrid Type-I and Type-II Censored Data

In this chapter, we first derive explicit expressions for the Maximum likelihood estimators (MLEs) of the parameters of Laplace distribution-based on a hybrid Type-I censored sample (Type-I HCS). We then derive the conditional moment generating functions (MGF) of the MLEs, and then use them to obtain the means, variances, and covariance of the MLEs. From the conditional MGFs, we also derive the exact conditional distributions of the MLEs, which are then used to develop exact conditional confidence intervals (CIs) for the parameters. Proceeding similarly, we obtain the MLEs of quantile, reliability, and cumulative hazard functions, and discuss the construction of exact CIs for these functions as well. By using the relationships between Type-I, Type-II, Type-I HCS, and hybrid Type-II censored samples (Type-II HCS), we develop exact inferential methods based on a Type-II HCS as well. Then, a Monte Carlo simulation study is carried out to evaluate the performance of the developed inferential results. Finally, a numerical example is presented to illustrate the point and interval estimation methods developed here under both Type-I HCS and Type-II HCS.