论文标题
多元Q-Polya和Q-Polya分布
Multivariate q-Polya and inverse q-Polya distributions
论文作者
论文摘要
考虑了包含指定数量不同有序颜色的球数的urn。通过假设从urn中q绘制特定颜色的球的概率与速率Q变化，Q-Polya urn模型的概率与图纸的数量和特定颜色的球数以及前面颜色的球总数，在先前的Q绘制中绘制。然后，在特定数量的Q绘制中和（b）中绘制的不同颜色的球数（a）的关节分布，直到得出特定数量的一定颜色的球。事实证明，这两个分布分别是多元polyA和逆Polya分布的Q分布。同样，由于urn中的初始球倾向于无穷大，因此多元q-polya和反向q-polya分布的限制分布分别为q-多属性和负q-胞源分布。
An urn containing specified numbers of balls of distinct ordered colors is considered. A multiple q-Polya urn model is introduced by assuming that the probability of q-drawing a ball of a specific color from the urn varies geometrically, with rate q, both with the number of drawings and the number of balls of the specific color, together with the total number of balls of the preceded colors, drawn in the previous q-drawings. Then, the joint distributions of the numbers of balls of distinct colors drawn (a) in a specific number of q-drawings and (b) until the occurrence of a specific number of balls of a certain color, are derived. These two distributions turned out to be q-analogues of the multivariate Polya and inverse Polya distributions, respectively. Also, the limiting distributions of the multivariate q-Polya and inverse q-Polya distributions, as the initial total number of balls in the urn tends to infinity, are shown to be q-multinomial and negative q-multinomial distributions, respectively.
