Some remarks on classical and bayesian reliability estimation of binomial and poisson distributions

The problems of estimating the reliability function and Pr{X₁+...+X_k ≤ Y} are considered. The random variables X’s and Y are assumed to follow binomial and Poisson distributions. Classical estimators available in the literature are discussed and Bayes estimators are derived. In order to obtain the estimators of these parametric functions, the basic role is played by the estimators of factorial moments of the two distributions.     

Bayesian Estimation of Regression Coefficients Under Extended Balanced Loss Function

Appreciating the desirability of simultaneously using both the criteria of goodness of fitted model and clustering of estimates around true parameter values, an extended version of the balanced loss function is presented and the Bayesian estimation of regression coefficients is discussed. The thus obtained optimal estimator is then compared with the least squares estimator and posterior mean vector with respect to the criteria like posterior expected loss, Bayes risk, bias vector, mean squared error matrix and risk function.     

Resolution of the Long-Term Performance Issues at the Waste Isolation Pilot Plant

The Waste Isolation Pilot Plant (WIPP) is a geological repository for disposal of U.S. defense transuranic radioactive waste. Built and operated by the U.S. Department of Energy (DOE), it is located in the Permian age salt beds in southeastern New Mexico at a depth of 655 m. Performance assessment for the repository's compliance with the 10,000-year containment standards was completed in 1996 and the U.S. Environmental Protection Agency (EPA) certified in 1998 that the repository meets compliance with the EPA standards 40 CFR 191 and 40 CFR 194. The Environmental Evaluation Group (EEG) review of the DOE's application for certification identified a number of issues. These related to the scenarios, conceptual models, and values of the input parameters used in the calculations. It is expected that these issues will be addressed and resolved during the first 5-year recertification process that began with the first receipt of waste at WIPP on March 26, 1999, and scheduled to be completed in March 2004.     

Bayesian analysis of the linear regression model with an edgeworth series prior distribution

The purpose of the present investigation 1s to observe the effect of departure from normahty of the prior distribution of regresslon parameters on the Bayman analysis of a h e a r regresslon model Assuming an Edgeworth serles prior distribution for the regresslon coefficients and gamma prior for the disturbances precision, the expressions for the posterlor distribution, posterlor mean and Bayes risk under a quadratic loss function are obtalned The results of a numerical evaluation are also analyzed     

Robust Bayesian analysis of generalized inverted family of distributions

ABSTRACT

In the current study we develop the robust Bayesian inference for the generalized inverted family of distributions (GIFD) under an ε-contamination class of prior distributions for the shape parameter α, with different possibilities of known and unknown scale parameter. We used Type II censoring and Bartholomew sampling scheme (1963) for the following derivations under the squared-error loss function (SELF) and linear exponential (LINEX) loss function : ML-II Bayes estimators of the i) parameters; ii) Reliability function and; iii) Hazard function. We also present simulation study and analysis of a real data set.     

Bayesian predictive analysis of the linear regression model with an edgeworth series prior distribution

In this paper we obtain the Bayes forecasts for the future observations on the dependent variable in the linear regression model when the regression coefficients have an Edgeworth series prior distribution. Furthermore, we consider the effect of departure from normality of the prior distribution of regression coefficients on the Bayes forecasts.     

BAYESIAN ANALYSIS OF THE LINEAR REGRESSION MODEL WITH NON-NORMAL DISTURBANCES

This paper considers the Bayesian analysis of a linear regression model with identically independently distributed non-normal disturbances. The distribution of disturbances is approximated by an Edgeworth series distribution with cumulants, of order higher than fourth, negligible. The posterior distribution of the regression coefficients vector is obtained under the assumption of a g-prior distribution for the parameters of the model. The Bayes estimator and its Bayes risk of the estimator are derived under a quadratic loss structure.     

Three-stage and ‘accelerated’ sequential procedures for the mean of a normal population with known coefficient of variation

Three-stage and ‘accelerated’ sequential procedures are developed for estimating the mean of a normal population when the population coefficient of variation (CV) is known. In spite of the usual estimator, i.e. the sample mean, Searls' (1964 Searls, DT. (1964). The utilization of a known coefficient of variation in the estimation procedure. J. Amer. Statist. Assoc, 50: 1225–1226.  ) estimator is utilized for the estimation purpose. It is established that Searls' estimator dominates the sample mean under the two sampling schemes.     

Stein rule prediction of the composite target function in a general linear regression model

This paper considers the problem of simultaneous prediction of the actual and average values of the dependent variable in a general linear regression model. Utilizing the philosophy of Stein rule procedure, a family of improved predictors for a linear function of the actual and expected value of the dependent variable for the forecast period has been proposed. An unbiased estimator for the mean squared error (MSE) matrix of the proposed family of predictors has been obtained and dominance of the family of Stein rule predictors over the best linear unbiased predictor (BLUP) has been established under a quadratic loss function.