2023/03/22 by V. V. Saenko, Saenko, Viacheslav V.
Energy · Engineering · #60E07 #Coal and Coke Industries Research #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Field-Flow Fractionation Techniques #Mining and Gasification Technologies #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2303.12488
openalex publication_date 2023/03/22 · openalex created_date 2023/03/25 · openalex updated_date 2026/07/28
The paper considers the problem of calculating the distribution function of a strictly stable law at x→∞. To solve this problem, an expansion of the distribution function in a power series was obtained, and an estimate of the remainder term was also obtained. It was shown that in the case α<1 this series was convergent for any x, in the case α=1 the series was convergent at N→∞ in the domain |x|>1, and in the case α>1 the series was asymptotic at x→∞. The case α=1 was considered separately and it was demonstrated that in that case the series converges to the generalized Cauchy distribution. An estimate for the threshold coordinate xεN was obtained which determined the area of applicability of the obtained expansion. It was shown that in the domain |x|\geqslant xεN this power series could be used to calculate the distribution function, which completely solved the problem of calculating the distribution function at large x.