Title: On shrunken estimators for the ratio of scale parameters in the exponential two-sample problem

Authors: Zuhair A. Al-Hemyari; Ashkan Khalifeh

Addresses: University of Nizwa, P.O. Box 33, PC 616, Nizwa, Oman ' Department of Statistics, Yazd University, Yazd, Iran

Abstract: In this paper, several shrunken estimators for the ratio of scale parameters of the exponential two-sample problem using two types of shrinkage functions are proposed. The first shrinkage function is based on the maximum likelihood estimator, and the second is based on the uniformly minimum variance unbiased estimator. The shrunken estimators expressions are obtained, computed and compared. Moreover, the performances of the shrunken estimators are evaluated. The proposed estimators dominate the classical estimators in the surprisingly large neighbourhood of the prior estimate of the ratio of scale parameters. Ultimately, using the data of a real experiment, the usefulness of these estimators are also illustrated.

Keywords: maximum likelihood estimator; MLE; negative exponential distribution; shrinkage estimator; stress-strength models; uniformly minimum variance unbiased estimator; UMVUE.

DOI: 10.1504/IJMMNO.2023.132291

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.3, pp.244 - 274

Received: 31 May 2022
Accepted: 27 Nov 2022
Published online: 17 Jul 2023 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article