Testing symmetry based on the extropy of record values

Abstract

In this paper, we first present the symmetric property of the extropy of record values and some characterisations of exponential distributions. Then a new test for symmetry of the continuous distribution is proposed based on a characterisation result. Our proposed test has an advantage that we do not need to estimate the centre of symmetry. Moreover, for a wide variety of alternative asymmetric distributions, Monte Carlo simulation shows that our test performs better than the competitor tests. Finally, two real data sets are used to illustrate the applicability of the proposed test by monitoring p-values of our test and its competitors.

Keywords:

• Extropy
• exponential distribution
• generalised lambda family
• record value
• test of symmetry

Mathematics Subject Classification (2010):

• Primary 62G30
• Secondary 63E10
• 62B10

Acknowledgments

The authors would like to thank two anonymous referees of the journal, Statistics. This work was supported by the National Nature Science Foundation of China (71871208, 71971204), the Anhui Provincial Natural Science Foundation (1908085MG236), and the Key Program Foundation from the Education Department of Anhui Province (KJ2018A0590, gxbjZD54).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors would like to thank two anonymous referees of the journal, Statistics. This work was supported by the National Nature Science Foundation of China [grant number 71871208], [grant number 71971204], the Anhui Provincial Natural Science Foundation [grant number 1908085MG236], and the Key Program Foundation from the Education Department of Anhui Province [grant number KJ2018A0590], [grant number gxbjZD54].