4032

Somayeh Ghafouri and...

مجله پژوهشهاي آماري ايران

Statistical Research and Training Center پژوهشكده آمار

2020

17

1

171-190

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

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 Li and Ri :i = 1; 2; : : : ; n (interval censoring). Our proposed method is based on finding the expected value of the conditional distribution of X given Li and Ri (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.