A Composite Hypothesis Test For Uniformity Based On Entropy

Many scholars have studied goodness-of-fit tests based on entropy, such as Vasicek(1976) studies the composite hypothesis test for normality based on entropy,Crzcgorzewski and Wirczorkowski(1999) studies the composite hypothesis test for exponentiality based on entropy, Dudewicz and Van Der Meulen(1981) studies the simple hypothesis test for uniformity based on entropy and so on.In the paper, the composite hypothesis test for uniformity based on entropy is proposed under the simple hypothesis test for uniformity based on entropy that is proposed by Dudewicz and Van Der Meulen(1981). First, the composite hypothesis test statistics for uniformity are proposed based on the good entropy estimates using SRS, the good properties of the test statistics are studied, and the composite hypothesis test method for uniformity is given. Then, the composite hypothesis test for uniformity based on entropy using SRS is extended to the case using RSS. And it is proved that the distribution of the composite hypothesis test statistics for uniformity based on entropy using SRS and RSS under the null hypothesis(ie, uniform distribution U(a,b) where a and b are unknown) is independent of the parameters a and b. Finally, A Monte Carlo simulation study is carried out to calculate the critical values of rejection region and the powers against seven alternatives of the composite hypothesis tests for uniformity based on entropy using SRS and RSS. The results show that the composite hypothesis test for uniformity based on entropy using RSS is more effective by comparing the powers of the composite hypothesis test for uniformity based on entropy using SRS and RSS.