2024 : 7 : 16
S.M.T.K. MirMostafaee

S.M.T.K. MirMostafaee

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0003-2796-4427
Education: PhD.
Faculty: Faculty of Mathematical Sciences
Address: Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Mazandaran‎, P.O‎. ‎Box 47416-1467‎, ‎Babolsar, ‎Iran‎
Phone: 01135302428


Bayesian Prediction of k-record Values Based on Hybrid Censored Sample from Exponential Distribution
A k-out-of-m system, Bayes predictors, Hybrid censoring, k-record values.
Researchers S.M.T.K. MirMostafaee


Let {X_i; i>=1} be an infinite sequence of independent identically distributed continuous random variables, then upper k-record process is defined in terms of the kth largest X yet seen. For a formal definition, let us follow Arnold et al. (1998, p. 43): For a fixed k, let T_{1,k} = k; R_{1(k)} = X_{1:k} and for n >=1 let T_{n,k}=min{j‎: ‎j>T_{n-1,k}‎, ‎X_j>X_{T_{n-1,k}-k+1:T_{n-1,k}}}, where X_{i:m} denotes the ith order statistic in a sample of size m. The sequence of upper k-records is then defined as R_{n(k)}=X_{T_{n,k}-k+1:T_{n,k}} for n>=1. For k = 1, the usual records are recovered. In reliability theory, the nth k-record statistic can be considered as the lifetime of a k-out-of-T_{m,k} system. One may consult Arnold et al. (1998) for an elaborate discussion on records and k-record values. In many life-testing and reliability experiments, the units are lost or removed from experimentation before failure. Data observed from such experiments are known as a censored sample. The two most common censoring schemes are termed as Type I and Type II censoring schemes. Consider a sample of m units placed on a lifetime experiment. In Type-I censoring scheme, the experiment continues up to a pre-specified time T. In Type-II censoring scheme, the experiment continues until a pre-specified number of failures r<=n occur. Hybrid censoring scheme is a mixture of Type-I and Type-II censoring schemes. In this scheme, the lifetime experiment terminates as soon as either the rth (r<= n is pre-fixed) failure or the pre-determined time T occurs. So far researchers studied prediction of records and k-records based on records and k-record values. Recently Ahmadi et al. (2012) discussed the new topic of Bayesian prediction of k-record statistics based on observed progressively censored exponential data. In this paper, based on hybrid censored observations, several Bayesian point and interval predictors for a future k-record value are obtained. The hybrid censored sample and the future