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The paper discusses the statistical inference problem of the compound Poisson vector process (CPVP) in the domain of attraction of normal law but with infinite covariance matrix. The empirical likelihood (EL) method to construct confidence regions for the mean vector has been proposed. It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law. The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix. Some simulation results are proposed to illustrate the method of the paper. [ABSTRACT FROM AUTHOR]

In this article, the author focus on the simple and yet very important case of making inference on the difference of two population means using the empirical likelihood approach of two sample compound Poisson process under infinite second moment. It is shown that the log empirical likelihood ratio statistic for the difference of two population means converges in distribution to χ (1) 2 as n → ∞. The simulation results show that the empirical likelihood ratio method is applicable under infinite second moment. [ABSTRACT FROM AUTHOR]

In this article, the author focuses on the simple and yet very important case of making inference on the difference of two population means using the empirical likelihood approach. It is shown that the log empirical likelihood ratio statistic for the difference of two population means converges in distribution to χ (1) 2 as n → ∞ when the two population are in the domain of attraction of normal law but have infinite variances. The simulation results show that the empirical likelihood ratio method is applicable under the infinite second moment condition. [ABSTRACT FROM AUTHOR]

In this article, we show that the log empirical likelihood ratio statistic for the population mean vector converges in distribution to χ (q) 2 as n → ∞ when the population is in the domain of attraction of normal law but has infinite covariance matrix. The simulation results show that the empirical likelihood ratio method is applicable under the infinite second moment condition. [ABSTRACT FROM AUTHOR]

The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored scheme. Different interval estimations are proposed. The interval estimations obtained are exact, approximate and bootstrap confidence intervals. Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations. Simulation results show that the confidence intervals (Cis) of exact and approximate methods are really better than those of the bootstrap method. [ABSTRACT FROM AUTHOR]

The Bayesian sampling plans for exponential distributions are studied based on type-II hybrid censored samples. The optimal Bayesian sampling plan is derived under a general loss function which includes the sampling cost, time-consuming cost, salvage value, and decision loss. It is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. Furthermore, for the conjugate prior distribution, the closed-form formula of the Bayes decision rule can be obtained under either the linear or quadratic decision loss. [ABSTRACT FROM AUTHOR]

In this paper, the reliability of a system is discussed when the strength of the system and the stress imposed on it are independent, non-identical exponentiated Pareto distributed random variables. Different point estimations and interval estimations are proposed. The point estimators obtained are maximum likelihood, uniformly minimum variance unbiased and Bayesian estimators. The interval estimations obtained are approximate, exact, bootstrap-p and bootstrap-t confidence intervals and Bayesian credible interval. Different methods and the corresponding confidence intervals are compared using Monte-carlo simulations. [ABSTRACT FROM PUBLISHER]