## Document Type

Report

## Source Publication Title

Technical Report 61

## Abstract

When there are available several point estimators of some parametric function, it would seem desirable to make a comparison among the estimators based on some measure of closeness to the true value. Along these lines, the concept of Pitman-closeness (PC) efficiency is introduced. Essentially, when comparing two estimators, PC efficiency gives the odds in favor of one of the estimators being closer to the true value in a given situation than is the other. The traditional method of comparison, i.e., mean squared (MS) efficiency is also considered. This paper presents graphical results based on simulation techniques which depict PC efficiencies as well as MS efficiencies of the following estimators of the reliability function R(t) of a 2-parameter exponential failure model: (i) the maximum likelihood estimator(R ^_MLE (t)), (ii) the minimum variance unbiased estimator (R ^_MVUE (t)) and (iii) a Bayesian/structural estimator (R ^_SE (t)). Based on the graphs, R ^_SE (t) is, in general, preferred (in the sense of having the best chance of being closest to the true value of R(t)) except (a) when R(t) is very high, in which case (R ^_MLE (t)) is preferred, and (b) when R(t) is moderate and the sample size is small to moderate, in which case R ^_MVUE (t) is preferred.

## Disciplines

Mathematics | Physical Sciences and Mathematics

## Publication Date

5-1-1977

## Language

English

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Lu, I-Le and Dyer, Danny D., "Efficiency Contours for Estimators of Reliability in a 2-Parameter Exponential Failure Model" (1977). *Mathematics Technical Papers*. 69.

https://mavmatrix.uta.edu/math_technicalpapers/69