Abstract
In this paper, we consider a general form for the underlying distribution and a general conjugate prior, and develop a general procedure for Bayesian estimation based on an observed multiply Type-II censored sample. The problem of predicting the order statistics from a future sample are also discussed from a Bayesian viewpoint. For the illustration of the developed results, the inverse Weibull distribution is used as example. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here.
Highlights
In reliability analysis, experiments often get terminated before all units on test fail due to cost and time considerations
It is well known that the marginal density function of the sth order statistic from a sample of size m from a continuous distribution with cumulative distribution function (CDF) F(x) and probability density function (PDF) f (x) is given, see Arnold et al [4], by fYs:m (y|θ )
To illustrate the inferential procedures developed in the preceding sections, we present a numerical study for the inverse exponential and inverse Rayleigh distributions as special cases of the inverse Weibull distribution when β = 1 and β = 2, respectively
Summary
Experiments often get terminated before all units on test fail due to cost and time considerations. Under this scheme, we observe only the j1th, j2th, · · · , jrth failure times Xj1:n, Xj2:n, ..., Xjr:n, where 1 ≤ j1 < j2 < · · · < jr ≤ n, and the rest of the data are not available. We observe only the j1th, j2th, · · · , jrth failure times Xj1:n, Xj2:n, ..., Xjr:n, where 1 ≤ j1 < j2 < · · · < jr ≤ n, and the rest of the data are not available Particular applications of such censoring are found in reliability theory and survival analysis.
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