论文标题
关于分支和出生和死亡过程中类似Sibuya的分布
On Sibuya-like distributions in branching and birth-and-death processes
论文作者
论文摘要
我们报告了与稀疏，自我分配性和分支过程有关的重尾类似Sibuya的分布的一些属性。通过任意阳性数字缩小到缩放的阴性整数随机变量的稀疏操作的扩展会导致一类新的概率分布，具有生成函数$ q（w）$表达为laplace transform $φ（1-W）$（1-W）$和概率质量质量质量质量$ P_N $满足简单的一步recrurnce Recrunce Recorcrence Recorrence Recorcrence Recorrence Recorrence Recorcrence Recrurnce Recorrence Recortrence $ P_ $ p_ $ p_ $ p_ $ p_ $ 1}我们表明，复合泊松 - 西布亚（Poisson-Sibuya）和转移的sibuya分布属于此类。利用同一马尔可夫财产存在于出生和死亡方程的固定解决方案中，我们确定了sibuya分布及其某些变体作为这些方程的特定解决方案。当整数价值的非负重尾随机变量具有有限的$ r $ - 绝对时刻（$ 0 <r <a <1 $）时，我们还建立了条件。
We report some properties of heavy-tailed Sibuya-like distributions related to thinning, self-decomposability and branching processes. Extension of the thinning operation of on-negative integer-valued random variables to scaling by arbitrary positive number leads to a new class of probability distributions with generating function $Q(w)$ expressible as a Laplace transform $φ(1-w)$ and probability mass function $p_n$ satisfying simple one step recurrence relation between $p_{n+1}$ and $p_n$. We show that the compound Poisson-Sibuya and the shifted Sibuya distributions belong to this class. Using the fact that the same Markov property is present in stationary solutions of the birth and death equations we identify the Sibuya distribution and some of its variants as particular solutions of these equations. We also establish condition when integer-valued non-negative heavy-tailed random variable has finite $r$-th absolute moment ($0 < r < a < 1$).
