Entropy-Based Tests of Uniformity

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.The power properties of an entropy-based test are investigated when used for testing uniformity on [0, 11. Percentage points and power against seven alternatives are reported. Compared with other tests of uniformity, the entropy-based test possesses good power properties for many alternatives. Some asymptotic null and alternative distributions are derived. For sample sizes up to 100 the table of percentage points provides a practical guide for using this test. A theory of entropy-based tests of distributional hypotheses other than uniformity is outlined.KEY WORDS: Entropy-based statistical inference; Tests of fit; Goodness of fit.

A two-sample empirical likelihood ratio test based on samples entropy

“…Vasicek (1976), Arizono and Ohta (1989), Dudewicz and Van Der Meulen (1981) as well as Ebrahami et al (1992) have demonstrated that the test statistic (2.4) with optimal values of m provides very powerful tests for normality, uniformity and exponentiality. Note that the authors obtained (2.4)-type test-statistics via estimation of the sample entropy (e.g., Vasicek 1976).…”

“…Note that, a very substantial body of literature has now grown around the asymptotic distribution problems involving the Vasicek's entropy estimator and the analogous statistics (e.g., Dudewicz and Van Der Meulen 1981;van Es 1992). However, it is generally recognized that even the asymptotic distribution of the statistic T mk by (2.4), which can depend on estimates of nuisance parameters of f 0 , is analytically difficult.…”

“…We apply the proposed approach to construct a powerful two-sample nonparametric likelihood ratio test based on samples entropy. Despite the fact that many statistical inference procedures have been developed to construct very efficient entropy-based tests for goodness-of-fit (e.g., Arizono and Ohta 1989;Dudewicz and Van Der Meulen 1981;Tian 2002, 2004;Tusnady 1977;Vasicek 1976;Vexler and Gurevich 2010;Zhang 2002), to our knowledge, there does not exist an inference procedure for two-sample empirical likelihood ratio comparisons based on samples entropy.…”

Performances of Shannon’s Entropy Statistic in Assessment of Distribution of Data

“…Different approaches were applied to estimate entropy and based on the new introduced estimators (e.g. modified Vasicek's estimator [37,38], Noughabi's entropy estimator [39]) new goodness-of-fit tests were developed and performances in testing the normal [40][41][42], lognormal [43], uniform [44][45][46], exponential [47], beta [47,48], Poisson [49], Weibull [43], Gamma [43], Pareto [50,51], Student and exponential distribution [52] were studied.…”

On testing homogeneity of variances for nonnormal models using entropy

“…Prescott (1976) using sensitivity contours showed that entropy test is considerably less sensitive to outliers than the one given by Shapiro-Wilk. Dudewicz and van der Muelen (1981) established a test for uniformity and they showed that this entropy test possesses good power properties for many alternatives. Menendez et al (1997) presented an estimator and a test statistic for goodness of fit based on Shannon's entropy and maximum entropy principle with order statistics.…”