Best Prediction Method for Progressive Type-II Censored Samples under New Pareto Model with Applications

Abstract

This paper describes two prediction methods for predicting the non-observed (censored) units under progressive Type-II censored samples. The lifetimes under consideration are following a new two-parameter Pareto distribution. Furthermore, point and interval estimation of the unknown parameters of the new Pareto model is obtained. Maximum likelihood and Bayesian estimation methods are considered for that purpose. Since Bayes estimators cannot be expressed explicitly, Gibbs and the Markov Chain Monte Carlo techniques are utilized for Bayesian calculation. We use the posterior predictive density of the non-observed units to construct predictive intervals. A simulation study is performed to evaluate the performance of the estimators via mean square errors and biases and to obtain the best prediction method for the censored observation under progressive Type-II censoring scheme for different sample sizes and different censoring schemes.

Bayesian Estimation of a New Pareto-Type Distribution Based on Mixed Gibbs Sampling Algorithm

“…Some scholars have conducted valuable research for the NP distribution in the literature, such as [10,11,15]. However, Bayesian methods may encounter challenges with high-dimensional, complex models, and big data in practice.…”

“…Thus, the fully conditional posterior distribution π(α|x 1 , x 2 , • • • , x r , β) of α, denoted as (15), is…”

“…In recent years, with the development of technologies such as big data analysis, artificial intelligence, and machine learning, the applications of the Gibbs sampling algorithm to solve Bayesian estimation problems has become increasingly common. Ahmed [15] proposed two prediction methods for predicting the censored units with progressive type II censored samples. The lifetimes under consideration are set to follow a new two-parameter Pareto distribution.…”

The Moore and Bilikam model and Burr XII sub-model under progressively type-II censoring scheme

“…− r m−1 units are excluded from the experiment. To read more about progressive type-II censoring, we refer to [12] and [1].…”

Progressive censoring schemes for marshall-olkin pareto distribution with applications: Estimation and prediction

“…[ 24 ] Used Bayes prediction to predict future values of a progressive censored sample under flexible Weibull distribution. [ 25 ] compare two prediction methods to predict the unobserved units from new Pareto model with progressive Type-II censoring scheme. In [ 30 ] the prediction of the remaining time for the generalized Pareto distribution under a progressive censored sample was considered.…”