Document Type
Thesis
Degree
Master of Science (MS)
Department
Statistics
Advisor's Name
Jie Mi
Advisor's Title
Committee Chair
Advisor's Name
Kai Huang
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.
Recommended Citation
Wang, Zeyi, "Inference about Reliability Parameter with Underlying Gamma and Exponential Distribution" (2011). FIU Electronic Theses and Dissertations. Paper 475.
http://digitalcommons.fiu.edu/etd/475