Abstract
Bayesian predictive probability density function is obtained when the underlying pop-ulation distribution is exponentiated and subjective prior is used. The corresponding predictive survival function is then obtained and used in constructing 100(1 – ?)% predictive interval, using one- and two- sample schemes when the size of the future sample is fixed and random. In the random case, the size of the future sample is assumed to follow the truncated Poisson distribution with parameter λ. Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn. Two illustrative examples are given, one of which uses simulated data and the other uses data that represent the breaking strength of 64 single carbon fibers of length 10, found in Lawless [40].
Highlights
The general problem of prediction may be described as that of inferring the values of unknown observables, or functions of such variables, from current available observations, known as informative sample. the problem of prediction can be solved fully within Bayes framework (Geisser [33] )
Special attention is paid to the exponentiated Burr type XII population, from which the data are drawn
Bayesian prediction bounds for order statistics of future observables from certain distributions, such as the exponential, Rayleigh, Weibull, Pareto and Lomax distributions, have been studied by several authors
Summary
The general problem of prediction may be described as that of inferring the values of unknown observables (future observations, known as future sample), or functions of such variables, from current available observations, known as informative sample. the problem of prediction can be solved fully within Bayes framework (Geisser [33] ). Prediction bounds for certain order statistics of samples from Burr type XII population, were obtained by Nigm [49], AL-Hussaini and Jaheen [14,15] and Ali Mousa and Jaheen [19]. A simple way of adding a parameter to a distribution is by exponentiation This goes back to Verhulst [62], who raised his 1838 [61] logistic cumulative distribution function (CDF) to a positive power. AL-Hussaini [8] estimated the parameters, SF and hazard rate function (HRF) under the general exponentiated model, using maximum likelihood and Bayes methods. He obtained prediction bounds of future observables based on the two-sample scheme under the exponentiated model.
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