Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...

Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...

This paper provides cumulative distribution function values for the standard multivariate normal distribution. The values are derived from a simulation model for the multivariate normal distribution, which can be run on any standard personal computer. Utilizing user-input distribution parameters, the model simulates the actual standard multivariate normal distribution. Since approximations of t...

Generalized variance is applied for determination of dispersion in a multivariate population and is a successful measure for concentration of multivariate data. In this article, we consider constructing confidence interval and testing the hypotheses about generalized variance in a multivariate normal distribution and give a computational approach. Simulation studies are performed to compare thi...

The empirical Bayes estimators of treatment effects in a factorial experiment were derived and their asymptotic properties were explored. It was shown that they were asymptotically optimal and the estimator of the scale parameter had a limiting gamma distribution while the estimators of the factor effects had a limiting multivariate normal distribution. A Bootstrap analysis was performed to ill...