Estimation Based on Progressive First-Failure Censored Sampling with Binomial Removals

Abstract

In this paper, the inference for the Burr-X model under progressively first-failure censoring scheme is discussed. Based on this new censoring were the number of units removed at each failure time has a discrete binomial distribution. The maximum likelihood, Bootstrap and Bayes estimates for the Burr-X distribution are obtained. The Bayes estimators are obtained using both the symmetric and asymmetric loss functions. Approximate confidence interval and highest posterior density interval (HPDI) are discussed. A numerical example is provided to illustrate the proposed estimation methods developed here. The maximum likelihood and the different Bayes estimates are compared via a Monte Carlo simulation study.

E-Bayesian Estimation for Rayleigh Model Using Progressive Type-II Censoring Data

“…For more details about the LINEX loss function, see for example, Calabria and Pulcini [5], Soliman et al [16] and El-Sagheer [6].…”

Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution

“…Here m and R = (R 1 , R 2 , • • • , R m ) are set in advance and ∑ m i=1 R i + m = n. To further illustrate, Figure 1 shows the process of the generation of progressive first-failure censored sample. In particular, pay attention that this censoring scheme has several special cases, one may refer to [10]. All the conclusions mentioned afterward are available to extend to those kinds of data, which is one of the advantages of progressive first-failure censoring.…”

Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

“…Hence, the number of patients who leave the experiment at a specified stage will follow the binomial distribution with probability of success (p). For this reason, [15,23] have considered the problem of estimation when the number of units removed at each stage follows a discrete uniform and binomial distributions, respectively, for progressively first-failure censored data.…”

“…[15] discussed the estimation problems of Pareto distribution when the lifetimes data are collected under a PFFCS with uniform removals. [23] derived the MLEs and Bayes estimators (BEs) of a parameter of Burr-X model under progressively first-failure censoring scheme with binomial removals (PFFCS-BR), were the number of units removed at each failure time has a discrete binomial distribution with certain probability p. Many several authors considered the problem of statistical inference based on Type-II progressive censoring with binomial random removals, see [24,25,10]. Recently, [8] discussed the Bayesian analysis of competing risk data under Type-II PCS where the number of units removed at each stage has a binomial distribution.…”

“…, m − 1, where m is predetermined before the life-testing, follows a binomial distribution S. K. ASHOUR, A. A. EL-SHEIKH AND A. ELSHAHHAT 49 with parameters n − m − ∑ i−1 j=1 r j and p, see [23]. Therefore,…”