COMMUNICATIONS IN STATISTICS—THEORY AND METHODS , VOL. , NO. , – http://dx.doi.org/./..
Equal-tailed and shortest Bayesian tolerance intervals based on exponential k-records A. Kiapoura and M. Naghizadeh Qomib a Department of Statistics, Babol Branch, Islamic Azad University, Babol, Iran; b Department of Statistics, University of Mazandaran, Babolsar, Iran
ABSTRACT
ARTICLE HISTORY
The problem of constructing the equal-tailed and shortest Bayesian tolerance intervals that control percentages in both tails of the exponential distribution based on k-record values is considered. Equal-tailed and shortest Bayesian tolerance factors are derived. Practical examples using real and simulated k-record values are given to illustrate the proposed results.
Received January Accepted July KEYWORDS
Exponential distribution; k-Record data; shortest Bayesian tolerance interval. MATHEMATICS SUBJECT CLASSIFICATION
F; F
1. Introduction Tolerance intervals are widely applied in quality control, pharmaceutical studies, manufacturing, and so on. A p-content, (1 − α)-confidence tolerance interval is constructed so that it would contain at least a proportion p of the population with confidence 1 − α. We refer to the interval simply as a (p, 1 − α) tolerance interval. Constructing tolerance intervals has received significant attention in recent years. A few of the many works that have recently appeared in this area are the following: Krishnamoorthy and Mathew (2009), Krishnamoorthy et al. (2011), Pathmanathan and Ong (2014), Young (2014), Naghizadeh Qomi et al. (2016), and Mbodj and Mathew (2015). For the exponential distribution and based on censored data, Goodman and Madansky (1962) presented equal-tailed guaranteed-coverage tolerance intervals and Fern´andez (2010) proposed a generalization of the classical perspective adopted by Goodman and Madansky (1962). Naghizadeh Qomi and Kiapour (2017) provided the shortest frequentist tolerance intervals for the exponential law on the basis of ordinary record values. In this paper, we construct the shortest Bayesian tolerance intervals for the exponential distribution based on k−record values. The rest of the paper is organized as follows. In Section 2, we state some preliminary definitions and results on k-record data. In Section 3, we compute the equaltailed and shortest Bayesian tolerance factors that control percentages in both tails. Two data set including a real k-record data and a simulated data are used for illustrating the results in Section 4. Finally, we conclude the paper and discuss some future problems in Section 5. CONTACT A. Kiapour Iran.
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Department of Statistics, Babol Branch, Islamic Azad University, Babol,
