论文标题
在$ Q $序列上定义的固定长度的成功运行 - 二进制试验
On Success runs of a fixed length defined on a $q$-sequence of binary trials
论文作者
论文摘要
我们研究了固定长度变化中固定长度的确切分布，该分布考虑了二进制试验的几何概率在几何上变化。随机变量$ e_ {n，k} $表示固定长度$ k $，$ 1 \ leq k \ leq n $的成功运行次数。 定理3.1给出了订单$ k $的type4 $ q $ binmial分布的概率质量函数（PMF）的封闭表达式。定理3.2和推论3.1给出了订单$ k $的type4 $ q $ binmial分布的概率质量函数（PMF）的递归表达式。概率生成函数和随机变量$ e_ {n，k} $的矩作为递归表达式获得。我们通过数值技术解决$ e_ {n，k} $的分布中的参数估计。在目前的工作中，我们考虑了一系列独立的二进制零和一个试验的序列，并不一定具有相同的分布，其概率根据几何规则而变化。通过枚举组合学获得的分布的精确和递归公式。
We study the exact distributions of runs of a fixed length in variation which considers binary trials for which the probability of ones is geometrically varying. The random variable $E_{n,k}$ denote the number of success runs of a fixed length $k$, $1\leq k \leq n$. Theorem 3.1 gives an closed expression for the probability mass function (PMF) of the Type4 $q$-binomial distribution of order $k$. Theorem 3.2 and Corollary 3.1 gives an recursive expression for the probability mass function (PMF) of the Type4 $q$-binomial distribution of order $k$. The probability generating function and moments of random variable $E_{n,k}$ are obtained as a recursive expression. We address the parameter estimation in the distribution of $E_{n,k}$ by numerical techniques. In the present work, we consider a sequence of independent binary zero and one trials with not necessarily identical distribution with the probability of ones varying according to a geometric rule. Exact and recursive formulae for the distribution obtained by means of enumerative combinatorics.
