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

Open Journal of Statistics 2020年第6期10卷 1057-1071页

作者： Zhengyuan Wei Tiankui Peng Xiaoya Zhou College of Science Chongqing University of Technology Chongqing China

In this paper, a new class of skew multimodal distributions with more flexible than alpha skew normal distribution and alpha-beta skew normal distribution is proposed, which makes some important distributions become its special cases. The statistical properties of the new distribution are studied in detail, its moment generating function, skewness coefficient, kurtosis coefficient, Fisher information matrix, maximum likelihood estimators are derived. Moreover, a random simulation study is carried out for test the performance of the estimators, the simulation results show that with the increase of sample size, the mean value of maximum likelihood estimators tends to the true value. The new distribution family provides a better fit compared with other known skew distributions through the analysis of a real data set.

关键词： Skew distribution multimodal distribution Alpha-Beta-Gamma Skew Normal distribution Fisher Information Matrix

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EQUATIONS FOR GRAIN SIZE distribution CURVE

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International Journal of Sediment Research 2004年第1期19卷 66-74页

作者： Prabhata K.SWAMEE,Nimisha SWAMEE Emeritus Fellow Indian Inst. of Tech. Roorkee Roorkee 247 667 India. B.E. (Civil) Student GZS College of Engrg. and Tech. Bhatinda 151 001 India.

The grain size distribution of particulate material is of particular interest in the field of sediment transport. The size distribution is described by various equations, however no equation is flexible enough to satisfy the grain size distribution data faithfully. Presented herein are the equations for unimodal and multimodal grain size distribution curves. A graphical method has been given to evaluate the parameters involved in these equations. The size distribution equation can be used to estimate many properties of sediment sample like number of sediment particles, surface area of the particles and hydraulic conductivity. It is hoped that the equations will find many applications in studying sedimentation processes.

关键词： Bimodal distribution Grain number Grain size gradation Hydraulic conductivity multimodal distribution Sediment Surface area Unimodal distribution

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