CAJ | 학술논문

探讨了取值在(0,1)区间上的随机变量的一种新的分布族,对其各阶矩给出了积分表达公式,证明了这种分布是指数族,并利用数学软件给出了这种分布的几种典型形态.与Beta分布相比,这种分布族的曲线形态更加丰富,同时,这种分布与Gamma分布又有着密切的关系.
탐토료취치재(0,1)구간상적수궤변량적일충신적분포족,대기각계구급출료적분표체공식,증명료저충분포시지수족,병이용수학연건급출료저충분포적궤충전형형태.여Beta분포상비,저충분포족적곡선형태경가봉부,동시,저충분포여Gamma분포우유착밀절적관계.
This article introduces a new family of distributions defined on the interval(0,1),and gives the integral representation to calculate its moments. It can be proved that the new distributions are exponential family. Further more,some typical shapes of the density curve have been shown in the article. The shapes that the new distribution densities can take are more abundant than the Beta distribution. At the same time,the new distribution is closely related to the Gamma distribution.