Document Type

Thesis

Degree

Master of Science (MS)

Department

Statistics

First Advisor's Name

Jie Mi

First Advisor's Title

Committee Chair

Second Advisor's Name

Kai Huang

Third Advisor's Name

Florence George

Keywords

Stress-Strength, Exponential Distribution, Gamma Distribution, UMVUE, MLE, MSE, Pivot, Bias

Date of Defense

9-30-2011

Abstract

The statistical inference about the reliability parameter R involving independent gamma stress and exponential strength is considered. Assuming the shape parameter of gamma is a known arbitrary real number and the scale parameters of gamma and exponential are unknown, the UMVUE and MLE of R are obtained. A pivot is proposed. Some inference about R derived from this pivot is presented. It will be shown that the pivot can be used for testing hypothesis and constructing condence interval. A procedure of constructing the condence interval for R is derived. The performances of the UMVUE and MLE are compared numerically based on extensive Monte Carlo simulation. Simulation studies indicate that the performance of the two estimators is about the same. The MLE is preferred because of the simplicity of its computation.

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