Journal of Statistics Applications & Probability

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In this article, we propose two test statistics based on the partial functional mean to test the conformity of a random sample with the Topp-Leone distribution. Characterization of the distribution based on the partial functional mean has been proven. The tests are formed as the integrated deviation (ID) or integral square deviation(ISD) between the sample and population partial functional means. Compared to the Kolmogorov-Smirnov (KS), Cramer-von Mises (CM), and Anderson-Darling (AD) tests, the proposed tests, say Dˆ n,1and Dˆ n,2, generally perform better in terms of their powers. The dependence of theDˆ n,1, Dˆ n,2,KS,CM, and AD tests on the skewness of the alternative is clear. In fact, we have found thatDˆn,2,KS,CM, and AD tests generally have higher powers than Dˆn,1 when testing against distributions with negative skewness and have lower powers when testing against distributions with positive skewness. We also noticed that Dˆn,2 outperforms the KS,CM, and AD tests when testing against negatively skewed alternatives and Dˆ n,1 outperforms all of these tests when testing against positively skewed alternatives. The percentiles and powers calculations were all based on Monte Carlo simulations.

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