Linear estimation for the extended exponential power distribution

Abstract

Tiao and Lund [The use of OLUMV estimators in inference robustness studies of the location parameter of a class of symmetric distributions. J Amer Statist Assoc. 1970;65(329):370–386] tabulated the coefficients of the best linear unbiased estimators (BLUEs) of location and scale for a particular family of symmetric distributions. This family was a reparameterization of the extended exponential power distribution (EEPD) with the shape parameter restricted to be greater than or equal to one. In this work, we consider the BLU estimation of the location and scale parameters of the EEPD when the shape parameter is one-third and one-half. We obtain closed-form expressions for the single and product moments of the order statistics when the shape parameter is in general in the form of a reciprocal of an integer. These expressions are then used to determine the BLUEs and the corresponding variances for complete samples of size 20 and less. We consider some other linear estimators of the location and scale parameters and then compare them with the BLUEs. Finally, we present a numerical example to illustrate the developed results.

Keywords:

• order statistics
• extended exponential power distribution
• location and scale parameters
• gamma distribution
• single moments
• product moments
• best linear unbiased estimators
• standard error

AMS Subject Classification:

• 62E15
• 62G05
• 62G30

Acknowledgements

We would like to acknowledge the associate editor and two anonymous referees for their comments and suggestions that improved this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.