Testing exponentiality based on the extropy of record values

Peihan Xiong; Weiwei Zhuang; Guoxin Qiu

doi:10.1080/02664763.2020.1840535

Testing exponentiality based on the extropy of record values

J Appl Stat. 2020 Oct 31;49(4):782-802. doi: 10.1080/02664763.2020.1840535. eCollection 2022.

Authors

Peihan Xiong¹, Weiwei Zhuang¹, Guoxin Qiu^{1

2}

Affiliations

¹ Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, People's Republic of China.
² Department of Business Administration, School of Business, Xinhua University of Anhui, Hefei, People's Republic of China.

Abstract

In this paper, we first present a characterization of exponential distribution based on the extropy of record values and next introduce a goodness-of-fit test for exponentiality. Monte Carlo simulation is used to compute the critical values of our proposed test for different sample sizes and significance levels. To show the advantage of the proposed test, we adopt 58 competitor tests and compute the adjusted power against different alternatives with distinct types of hazard function. The power results show that our proposed test has superior adjusted power if the alternatives have increasing failure rates or bathtub decreasing-increasing failure rates, especially when the sample size is small. Finally, three real examples are used to illustrate the applicability and robustness of our proposed test by monitoring the p-values of the tests.

Keywords: 62B10; Adjusted power; Monte Carlo simulation; Primary 62G30; Secondary 63E10; exponentiality test; extropy; record value.

Grants and funding

This work was supported by the National Nature Science Foundation of China (71871208, 71971204), the Anhui Provincial Natural Science Foundation (1908085MG236, gxbjZD54).