Abstract
The Pareto Type-II model is considered here from which, the observable is to be predicted by using Bayesian approach. The Bayes prediction bound lengths are obtained for Type-I progressive hybrid censored data. Both One-sample and Two-sample Bayes prediction scenario has included in the present study. Both known and unknown cases of the scale parameter have considered in the present study. A comparison also has made with the asymptotic interval estimates, are made-up from the Fisher information matrix. Performance of the different methods has studied by simulation and a real data set.
Highlights
The underlying distribution is a mixture of the Exponential distribution with scale parameter α, and the given scale parameter α is distributed as Gamma density with parameters θ and σ
Let us suppose l1 and l2 be the lower and upper Bayes prediction bound limits, 100(1− )% Bayes prediction bound length for the future observation Y corresponding to the parameter θ, under Type-I progressive hybrid censoring scenario is obtained by solving following equation
If l1 and l2 be the lower and upper Bayes prediction bound limits, 100(1 − )% Bayes prediction bound limits for the future observation Y under Type-I progressive hybrid censoring corresponding to the parameters Θ (= θ, σ), are obtained by solving following inequality e−θ log l1 +σ σ
Summary
The underlying distribution is a mixture of the Exponential distribution with scale parameter α, and the given scale parameter α is distributed as Gamma density with parameters θ and σ. Bound Lengths On Type-I Progressive Hybrid Censoring system and forecasting of the temperature records etc. Okasha (2014) concerned in his article about E-Bayesian method for computing the estimates of the reliability parameters of the Lomax distribution by using conventional Type-II censored data. Based on the right ordered sample data, central coverage bound lengths under the Bayesian inferences was inspected by Prakash (2014) for the Lomax model. Prakash (2017) was discussed about some statistical inference based on Progressive Type-II censored data for two-parameter Pareto distribution. The goal of the present study is to investigate the properties of Bayes prediction bound lengths for unknown parameters of the underlying distribution. Two different scenarios have used for predicting future observations on Type-I Progressive hybrid censored data for known & unknown cases of scale parameter. A comparison has been made with the asymptotic interval estimates obtained from Fisher information matrix by following Park and Balakrishnan (2009)
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