Some two-sample tests for simultaneously comparing both parameters of the shifted exponential models

Abstract

This paper investigates the power performance of five tests, including improved versions of two existing tests, for jointly testing the equality of origin and scale parameters of two samples from a shifted (two-parameter) exponential distribution. The power of the test varies with a shift in either or both of the two parameters. Therefore, a power surface is observed for various tests. Different tests are optimal for different shift sizes. This paper also compares the volume under the five tests’ power surfaces to determine an overall best when the shift size is unknown. The generalized likelihood ratio (GLR) test, the Bayoud and Kittaneh test based on Weitzman’s overlapping coefficient, recently designed Max and Distance tests, and an improved likelihood-based procedure are compared. The shifted exponential distribution is often an appropriate probability model for the lifetime of a product with a warranty, high voltage current in specific semiconductor transistors, and military personnel vehicles’ mileages that failed in operation. The number of survival days for patients with irreversible lung cancer often follows the same distribution. This distribution plays a vital role in the engineering and biomedical sciences. We observe that the newly designed tests and the exact GLR test are almost always preferable to the other tests. We illustrate the proposed exact test procedures with two practical examples.

Keywords:

• Combination of tests
• generalized likelihood ratio
• Monte-Carlo
• nuisance parameters
• power surface
• two-parameter (shifted) exponential

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The research was supported by the Ministry of Higher Education (MoHE) Malaysia through Fundamental Research Grant Scheme project FRGS/1/2019/STG06/UTAR/02/2.