JSM 2004 - Toronto

Abstract #301311

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Activity Number: 189
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Physical and Engineering Sciences
Abstract - #301311
Title: Prediction Bounds for the Number of Successes in a Sequence of Markov-dependent Bernoulli Trials
Author(s): Florian Rueck*+
Companies: University of Missouri, Rolla
Address: 1805 Ashwood Dr. Apt. D, Rolla, MO, 65401,
Keywords: Bernoulli trials ; Markov-dependent ; prediction intervals ; maximum likelihood predictive density
Abstract:

A generalization of a prediction interval procedure for the binomial distribution to the case of the binomial distribution with Markov-dependent trials is considered. Several different methods have been developed for the binomial distribution but only a method proposed by Lejeune and Faulkenberry is applied to the case of the binomial distribution with dependent trials. Given n observations from a binomial distribution with Markov-dependent trials, it is of interest to find an interval estimate such that the number of successes in a future set of trials is contained in the interval with a certain level of confidence. A simulation study was considered to investigate the coverage probabilities of the prediction bounds, which are based on the maximum likelihood predictive density. The use of estimators due to Klotz, Price, Kim, and Bai in place of the MLE, is considered because the MLEs cannot be expressed in a closed form.

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