One-Sample Bayesian Predictive Interval of Future Ordered Observations for the Pareto Distribution
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Nigm et al. (2003, statistics 37: 527–536) proposed Bayesian method to obtain predictive interval of future ordered observation Y (j) (r < j≤ n ) based on the right type II censored samples Y (1) < Y (2) < ... < Y (r) from the Pareto distribution. If some of Y (1) < ... < Y (r-1) are missing or false due to artificial negligence of typist or recorder, then Nigm et al.’s method may not be an appropriate choice. Moreover, the conditional probability density function (p.d.f.) of the ordered observation Y (j) (r < j ≤ n ) given Y (1) <Y (2) < ... < Y (r) is equivalent to the conditional p.d.f. of Y (j) (r < j ≤ n ) given Y (r). Therefore, we propose another Bayesian method to obtain predictive interval of future ordered observations based on the only ordered observation Y (r), then compares the length of the predictive intervals when using the method of Nigm et al. (2003, statistics 37: 527–536) and our proposed method. Numerical examples are provided to illustrate these results.
Keywordsright type II censored sample Bayesian predictive interval pareto distribution one-sample problem
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