Showing papers by "Barry C. Arnold published in 1998"

Joint Confidence Sets for the Mean and Variance of a Normal Distribution

Abstract: The standard example of an exact joint confidence set provided in elementary textbooks involves normal data., In addition textbooks provide a variety of asymptotic approximate joint confidence sets for (μ, σ2) in such a setting. What is lacking, and what is provided in this article, is a comparative study of the size and actual performance of these confidence sets. A mild surprise arises in the comparison. If the sample size is 100 or more, the asymptotic confidence regions, in addition to being more robust to violations of distributional assumptions, actually outperform the exact region in terms of expected area of the regions.

Bayesian analysis for classical distributions using conditionally specified priors

Abstract: SUMMARY. Certain conditionally specified joint distributions prove to be convenient conjugate prior families for classical multiparameter problems. Although the number of hyperparameters is large, assessment is shown to be reasonably straightforward, often involving the use of routine regression programs. Examples are provided involving both informative and diuse prior information.

Distributions most nearly compatible with given families of conditional distributions

Abstract: Consider a discrete bivariate random variable (X, Y) with possible values 1, 2, ...,I forX and 1, 2, ...J forY. Suppose that putative families of conditional distributions, forX given values ofY and ofY given values ofX, are available. After reviewing conditions for compatibiity of such conditional specifications of the distribution of (X, Y), attention is focussed on the incompatible case. The Kullback-Leibler information function is shown to provide a convenient measure of inconsistency. Using it, algorithms are provided for computing the joint distribution for (X, Y) that is least discrepant from the given inconsistent conditional specifications. Other discrepancy measures are briefly discussed.

Some alternative bivariate gumbel models

Abstract: For modelling bivariate extremes, the classical bivariate Gumbel models are limited in their flexibility for fitting real world data sets. Alternative models, derived via conditional specification, are introduced in the current paper. A key difference between the classical models and the conditional specification models is to be found in the sign of the correlation between the variables in the models: non-negative for classical models, non-positive for conditionally specified models. Copyright © 1998 John Wiley & Sons, Ltd.