Estimation of common location parameter of two exponential populations based on records

ABSTRACT

Consider the problem of estimating the common location parameter of two exponential populations using record data when the scale parameters are unknown. We derive the maximum likelihood estimator (MLE), the modified maximum likelihood estimator (MMLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the common location parameter. Further, we derive a general result for inadmissibility of an equivariant estimator under the scaled-squared error loss function. Using this result, we conclude that the MLE and the UMVUE are inadmissible and better estimators are provided. A simulation study is conducted for comparing the performances of various competing estimators.

KEYWORDS:

• Exponential distribution
• Maximum likelihood estimator
• Uniformly minimum variance unbiased estimator
• Upper record values.

MATHEMATICS SUBJECT CLASSIFICATION:

• 2010: Primary 62F10
• Secondary 62G32

Acknowledgements

The authors are thankful to the anonymous referees and the editor for their valuable suggestions which have improved the original manuscript.