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The Alpha-Beta-Gamma Skew Normal Distribution and Its Application

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Document pages: 15 pages

Abstract: In this paper, a new classof skew multimodal distributions with more flexible than alpha skew normaldistribution and alpha-beta skew normal distribution is proposed, which makessome important distributions become its special cases. The statisticalproperties of the new distribution are studied in detail, its moment generatingfunction, skewness coefficient, kurtosis coefficient, Fisher informationmatrix, maximum likelihood estimators are derived. Moreover, a randomsimulation study is carried out for test the performance of the estimators, thesimulation results show that with the increase of sample size, the mean valueof maximum likelihood estimators tends to the true value. The new distributionfamily provides a better fit compared with other known skew distributionsthrough the analysis of a real data set.

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