Cumulative residual entropy applied to testing uniformity

Abstract

We present properties of the cumulative residual entropy and then propose a test for uniformity. An approximation of distribution of the test statistic is derived. The mean, variance, and the asymptotic null distribution of the test statistic are presented. Percentage points and power against seven alternatives are reported. The results of a simulation study show that the test is competitive in terms of power. Moreover, the proposed statistic is easy to compute and can be approximated by the beta distribution.

Keywords:

• Cumulative residual entropy
• testing uniformity
• empirical distribution function
• Monte Carlo methods
• test power