Shrinkage Estimators and Their Efficiency in Reliability Calculations

• Activity Number: 564
• Type: Contributed
• Date/Time: Thursday, August 6, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Mohammed A. Shayib*+ and Aliakbar Montazer Haghighi
• Companies: Prairie View A&M University and Prairie View A&M University
• Keywords: Reliability ; Probability Distributions ; MLE ; Shrinkage Estimators ; Ratio of parameters & sizes ; Simulation

Abstract

The inference about R = P (Y < X) or estimating its value, assuming X and Y to be independent and identically distributed random variables, has been extensively studied. Assuming there is a prior value of R, we will utilize this information to develop what is called "shrinkage estimators." These were introduced by Thompson (1968). Distribution functions such as Burr Type X, Exponential, and Weibull have been taken as parent distributions for X and Y. In this paper, we consider the Maximum Likelihood Estimation, Shrinkage Estimation Procedures, and Method of Moments, to estimate the unknown parameters of the underlined distributions. In particular, we will observe how well the shrinkage estimators will compare to the MLE based on the estimated mean squared error (MSE) and efficiency criteria. Also, a comparison among the estimators will be done based on sample size and parameters ratio.