Advances and Applications in Statistics
Volume 53, Issue 2, Pages 165 - 177
(August 2018) http://dx.doi.org/10.17654/AS053020165 |
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A NEW GOODNESS OF FIT TEST FOR THE BETA DISTRIBUTION BASED ON THE EMPIRICAL LAPLACE TRANSFORM
Mahmoud Riad and Ola Farouk Abd El Mabood
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Abstract: In this paper, a new goodness of fit test for the beta distribution that employs the empirical Laplace transform is conducted. The proposed test is formed using differential equation of Kummer, which considers Laplace transform as a solution for measuring the discrepancy from zero. The consistency of the test and its asymptotic distribution under the null hypothesis are investigated theoretically. The decay of the test weight function tends to infinity, and the test statistics approach limit values are related to the first nonzero component of Neyman’s smooth test for the beta distribution. For practical investigation of this test, a simulation study is conducted to compare the new test with other well known tests for the beta distribution. The significance of this paper is derived from the literature lack of statistical inference regarding the beta distribution, particularly for the practical issues. |
Keywords and phrases: beta distribution, goodness of fit test, empirical Laplace transform, smooth test. |
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