چکیده:
In this paper, we study the performance of estimators of parameters
of two-parameter exponential distribution based on upper records. The
generalized likelihood ratio (GLR) test was used to generate preliminary test
estimator (PTE) for both parameters. We have compared the proposed estimator
with maximum likelihood (ML) and unbiased estimators (UE) under
mean-squared error (MSE) and Pitman measure of closeness (PMC). Analytical
as well as graphical methods are used to show the range of parameter
in which PTE performs better than ML and UE. Results demonstrate that
in the case of that prior information is not too far from its real value, the
PTE is superior in compare with ML and UE based on both MSE and PMC
criteria. The results of the paper will be useful in estimation with record
data in life testing experiments.
خلاصه ماشینی:
We have compared the proposed esti-mator with maximum likelihood (ML) and unbiased estimators (UE) undermean-squared error (MSE) and Pitman measure of closeness (PMC).
For ex- ample, Chiou(1987) found the PTE of reliability in a life-testing model and Chiou (1988) utilized preliminary test estimation for the scale parameter of the extreme value distribution.
Baklizi (2005) and Kibria and Saleh (2010) have applied the method of PTE for estimating the scale parameter of exponential distribution based on censored data.
In what follows, we consider the upper records from two-parameter exponential distribution and compute the MLE, UE and PTE of the scale and location parameters in order to see which one is Pitman closer to the target parameter.
2 Preliminary Test Estimation In this section, we study the estimation of the location and scale parameters for the exponential distribution based on records, which include ML and UE, as well as PTE.
3 Comparison Based on PMC In this section, we compare the proposed estimators via Pitman measure of closeness.
All the probabilities of closeness depend on the number of records,∆sand the size of test, so for diferent values of nandα, the graphs of GPC and PMC have been drawn for∆s∈ (0,3), in Figures 1 and 2.
⃝c 2014, SRTC Iran 4 MSE Evaluations Considering the MSE as a criterion of comparison, in this section we compare the performance of the proposed estimators based on mean-squared relative efciency (MRE).