Inference about Reliability Parameter with Underlying Gamma and Exponential Distribution

OF THE THESIS INFERENCE ABOUT RELIABILITY PARAMETER WITH UNDERLYING GAMMA AND EXPONENTIAL DISTRIBUTION by Zeyi Wang Florida International University, 2011 Miami, Florida Professor Jie Mi, Major Professor 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 confidence interval. A procedure of constructing the confidence 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.