Non-Bayesian Estimation and Prediction under Weibull Interval Censored Data

AuthorsFatemeh Yousefzadeh,,,
Journalپژوهش های آماری ایران-Journal of Statistical Research of Iran
Page number171-190
Serial number17
Volume number1
Paper TypeFull Paper
Published At2023
Journal GradeScientific - research
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of
Journal Indexisc

Abstract

In this paper, a one-sample point predictor of the random variable X is studied. X is the occurrence of an event in any successive visits $L_i$ and $R_i$ :i=1,2…,n (interval censoring). Our proposed method is based on finding the expected value of the conditional distribution of X given $L_i$ and $R_i$ (i=1,2…,n). To make the desired prediction, our approach is on the basis of approximating the unknown Weibull parameters using the mid-point approximation and approximate maximum likelihood (AML). After obtaining the parameter estimation, the prediction of X can be made. Moreover, the 95% bootstrap confidence intervals of unknown parameters and the 95% bootstrap prediction bounds of X are presented. The performance of the proposed procedure based on the mean squared error (MSE) and the average width (AW) of the confidence interval is investigated by employing Monte Carlo simulation. A Real data set is also studied to illustrate the proposed procedure.

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tags: Approximate maximum likelihood estimator, Bootstrap samples, interval censoring, mean squared prediction error, mid-point approximation, monte Carlo simulation, one-sample prediction.