Estimation and Prediction for the Half-Normal Distribution based on Progressively Type-II Censored Samples

Abstract

In this paper, estimation and prediction problems are discussed for the half-normal distribution under a progressively Type-II censoring scheme. This study focuses on two statistical inferential problems. In the first part of the study, several point estimators and confidence intervals are obtained for the scale parameter of the half-normal distribution. In the second part, several predictors and predictive intervals are derived for the removed failure times. A Monte Carlo simulation study is performed to discuss the mean squared error (mean squared prediction errors) and bias of estimates (predictors). The coverage probabilities and average length of the confidence and predictive intervals are simulated and a numerical example is provided.

Keywords

• confidence intervals
• half-normal distribution
• maximum likelihood estimator
• Monte Carlo simulation
• pivotal estimator
• prediction