Testing symmetry based on the extropy of record values
Peihan Xiong, Weiwei Zhuang, Guoxin Qiu
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.
Topics & Concepts
MathematicsSymmetry (geometry)Monte Carlo methodVariety (cybernetics)Test (biology)Exponential distributionExponential functionDistribution (mathematics)Statistical physicsSymmetric probability distributionApplied mathematicsAlgorithmStatisticsProbability distributionMathematical analysisGeometryPhysicsBiologyPaleontologyStatistical Distribution Estimation and ApplicationsBayesian Methods and Mixture ModelsAdvanced Statistical Process Monitoring