The distributions of sum, minima and maxima of generalized geometric random variables
The distributions of sum, minima and maxima of generalized geometric random variables
复制标题
广义几何随机变量的总和、最小值和最大值的分布
DOI：
10.1007/s00362-014-0632-4
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发表时间：
2015
影响因子：
1.3
通讯作者：
S. Eryilmaz
中科院分区：
文献类型：
--
作者：
F. Tank;S. Eryilmaz
阶数几何分布是已知几何分布的推广，它是具有成功概率的Bernoulli试验中直到第一次连续成功的试验次数的分布。在本文中，它表明，这种广义分布可以表示为一个离散的相位型分布。利用这一表示沿着并结合相型分布的封闭性质，得到了两个具有序几何分布的独立随机变量的和、最小值和最大值的分布。数值结果来说明计算细节。
Geometric distribution of orderas one of the generalization of well known geometric distribution is the distribution of the number of trials until the firstconsecutive successes in Bernoulli trials with success probability. In this paper, it is shown that this generalized distribution can be represented as a discrete phase-type distribution. Using this representation along with closure properties of phase-type distributions, the distributions of sum, minima and maxima of two independent random variables having geometric distribution of orderare obtained. Numerical results are presented to illustrate the computational details.