论文标题
类型$ 1 $，$ 2 $，$ 3 $和$ 4 $ $ Q $ - 负二项式订单$ K $
Type $1$, $2$, $3$ and $4$ $q$-negative binomial distribution of order $k$
论文作者
论文摘要
我们研究了等待时间的分布，以$ k $的负二项式分布的变化。一种变化在成功的运行中应用不同的枚举方案。另一个案例考虑了二进制试验，其概率在几何上有所不同。我们调查了$ r $ $ - 在二进制试验的$ q $序列中的指定长度（至少，至少，至少，至少，至少，至少，$ \ ell $ overplapping）成功运行成功的等待时间的确切分布。主要定理是类型$ 1 $，$ 2 $，$ 3 $和$ 4 $ Q $ Q $ - 阴性的订单$ k $和$ Q $ Q $ - 负二项式分布$ \ ell $ boverplapping案例中的订单$ k $。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。通过枚举组合制剂获得的分布的确切公式。
We study the distributions of waiting times in variations of the negative binomial distribution of order $k$. One variation apply different enumeration scheme on the runs of successes. Another case considers binary trials for which the probability of ones is geometrically varying. We investigate the exact distribution of the waiting time for the $r$-th occurrence of success run of a specified length (non-overlapping, overlapping, at least, exactly, $\ell$-overlapping) in a $q$-sequence of binary trials. The main theorems are Type $1$, $2$, $3$ and $4$ $q$-negative binomial distribution of order $k$ and $q$-negative binomial distribution of order $k$ in the $\ell$-overlapping case. 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 formulae for the distributions obtained by means of enumerative combinatorics.
