2023/02/15 by Muneya Matsui, Toshiro Watanabe, Matsui, Muneya +1
Business, Management and Accounting · Engineering · Mathematics · #60E07 #60G70 #62F12 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Reliability and Maintenance Optimization #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2302.07487
openalex publication_date 2023/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We completely characterize Δ- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, Δ-subexponentiality of infinitely divisible distributions is characterized with new conditions, and local subexponentiality is newly characterized in the two-sided case. In the process closedness properties of these subexponentialities are derived, particularly for distributions on \R. Most results are obtained by exploiting monotonic-type assumptions. We apply our results to distributions of supremum of a random work and a randomly stopped iid sum.