Parameter Estimation and Prediction of Future Failures in the Log-Logistic Distributions Based on Hybrid-Censored Data

Abstract

The main purpose of this thesis is to study the prediction of future observations of a Log-Logistic distribution from Hybrid Censored Samples. We will study parameter point estimation, interval estimation, different point predictors will be formed such as Maximum Likelihood Predictor (MLP), Best Unbiased Predictor (BUP), and Conditional Median Predictor (CMP). Different Prediction intervals will be constructed such as Intervals based on Pivotal quantities, and High-Density Intervals (HDI). A simulation study will be run using the R software to investigate and compare the performance of all point predictors and prediction intervals. It is observed that the (BUP) is the best point predictor and the (HDI) is the best prediction interval.