Masters Theses


"A generalization of a prediction interval procedure for the binomial distribution to the case of the binomial distribution with dependent trials is considered. Several different methods have been developed for obtaining prediction intervals for the binomial distribution. An unpublished study by Vlieger and Samaranayake has shown that two of these methods achieve coverage probabilities close to nominal levels. The proposed method is an extension of one of these methods and is based on the maximum likelihood predictive density proposed by Lejeune and Faulkenberry. A simulation study was carried out to investigate the coverage probabilities of the proposed prediction bounds.

This method requires the availability of a closed form expression for the maximum likelihood parameter estimates. For the binomial distribution with dependent trials, three estimators asymptotically equivalent to the maximum likelihood estimators (MLE) due to Klotz, Price, and Kim and Bai are available. The use of these estimators, in place of the MLE, is considered because the MLEs cannot be expressed in a closed form. Simulation results show the prediction bounds based on Klotz’s estimator exhibit reasonable coverage probabilities in the case of the binomial distribution with dependent trials"--Abstract, page iii.


Samaranayake, V. A.

Committee Member(s)

Gadbury, Gary L.
Bryant, Richard Ralph


Mathematics and Statistics

Degree Name

M.S. in Mathematics


University of Missouri--Rolla

Publication Date

Spring 2003


viii, 82 pages

Note about bibliography

Includes bibliographical references (page 81).


© 2003 Florian Sebastian Rueck, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Binomial distribution
Prediction (Logic)

Thesis Number

T 8240

Print OCLC #


Included in

Mathematics Commons