Entropy-based Goodness-of-fit Test for Positive Stable Law

A goodness-of-fit test for positive stable law is proposed. For this mean, the Kullback-Leibler distance measure, as a basic tool in entropy theory, is considered. A simulation study is performed to compare the performance of the proposed method and old ones that suggested by Shkol’nik [6]. The results reveal that the introduced approach here shows more performance, in the sense of the test statistic empirical power, than the Shkol’nik [6] treatment in both cases: 1both exponent and scale parameters of positive stable law are unknown and sample size is small; 2exponent parameter is known. Real data application is illustrated to show proposed approach’s superior performance versus the old method.