论文标题
严格稳定定律在零附近的概率密度和分布函数的计算
The calculation of the probability density and distribution function of a strictly stable law in the vicinity of zero
论文作者
论文摘要
在$ x \ to0 $中计算严格稳定法的概率密度和分布功能的问题。这些值的扩展为幂序列以解决此问题。结果表明，在$α<1 $的情况下，所获得的系列是$ x \ to0 $的渐近系列，在$α> 1 $的情况下，它们是收敛的，在域中$α= 1 $的情况下，这些系列收敛于非对称的Cauchy分布。已经表明，在$ x \ to0 $时，获得的扩展可以成功地用于计算严格稳定法律的概率密度和分布函数。
The problem of calculating the probability density and distribution function of a strictly stable law is considered at $x\to0$. The expansions of these values into power series were obtained to solve this problem. It was shown that in the case $α<1$ the obtained series were asymptotic at $x\to0$, in the case $α>1$ they were convergent and in the case $α=1$ in the domain $|x|<1$ these series converged to an asymmetric Cauchy distribution. It has been shown that at $x\to0$ the obtained expansions can be successfully used to calculate the probability density and distribution function of strictly stable laws.
