Statistical Inference for Lognormal Distribution with Type-I Progressive Hybrid Censored Data

Abstract

This article deals with problems of estimation and prediction under classical and Bayesian approaches when lifetime data following a lognormal distribution are observed under type-I progressive hybrid censoring. We first obtain maximum likelihood estimates, Bayes estimates, and corresponding interval estimates of unknown lognormal parameters. We then develop predictors to predict censored observations and construct prediction intervals. Further, we analyze two real data sets and conduct a simulation study to compare the performance of proposed methods of estimation and prediction. Finally, optimal censoring schemes are constructed under cost constraints and a conclusion is presented. KEY WORDS AND PHRASESEM algorithm; MH algorithm; prediction; HPD interval; equal-tail interval; optimal censoring CONTACT Sukhdev Singh

Estimation and prediction using classical and Bayesian approaches for Burr III model under progressive type-I hybrid censoring

“…This section deals with the use of best unbiased predictor (BUP) to predict the z ðijÞ observations. A statistic ẑðijÞ is said to be BUP of z ðijÞ , if ðẑ ðijÞ À z ðijÞ Þ, called the prediction error has a mean zero and further prediction error variance, say Varðẑ ij À z ðijÞ Þ is less than or equal to that of any other unbiased predictor of z ðijÞ , see Dey et al (2016) and Sen et al (2019). Thus the BUP of z ðijÞ can be obtained as ẑðijÞ ¼ E½z ðijÞ j x, j ¼ 1; 2; .…”

“…Therefore if statistical inferences for the observed data are obtained under this censoring then the same inferences can be generalized to the particular cases. In the existing literature statistical inferences under progressive type-I hybrid censoring have been obtained by Cramer and Balakrishnan (2013) for exponential distribution, Golparvar and Parsian (2016) and Noori et al (2016) for Burr type XII distribution, Tomer and Panwar (2015) for maxwell distribution, and Sen et al (2019) for lognormal distribution. In the present work we will focus on Burr type III distribution.…”

Bayesian Estimation and Prediction for Exponentiated Inverted Topp-Leone Distribution

“…See for example, AL-Hussaini and Hussein [4] studied Bayesian prediction of the future observation from exponentiated populations based on one and two-sample prediction with fixed and random sample size. Also, Singh et al [18], Sen et al [16] and Ateya et al [7] studied the onesample and two-sample prediction schemes for a future observation from Burr X distribution based on a unified hybrid censoring scheme using the likelihood and the Bayesian prediction methods.…”

Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

“…Furthermore, we denoted by X 1:m:n , X 2:m:n , • • • , X m:m:n . See References [3][4][5][6]. The joint probability density function (PDF) of PrCS data can be expressed by f (x 1:m:n , x 2:m:n , • • • , x m:m…”