Physical Sciences and Mathematics Commons^™

A Comparison Of Estimation Procedures For The Beta Distribution, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The beta distribution may be used as a stochastic model for continuous proportions in many situations in applied statistics. This thesis was concerned with estimation of the parameters of the beta distribution in three different situations.

Three different estimation procedures-the method of moments, maximum likelihood, and a hybrid of these two methods, which we call the one-step improvement-were compared by computer simulation, for beta data and beta data contaminated by zeros and ones. We also evaluated maximum likelihood estimation in the context of censored data, and Newton's method as a numerical procedure for solving the likelihood equations …

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.