Comparing Compound Poisson Distributions by Deficiency: Continuous-Time Case

In the paper, we apply a new approach to comparison of distributions sums random variables case Poisson sums. This was proposed in our previous work (Bening, Korolev, 2022) and is based on concept statistical deficiency. Here, introduce continuous analog under consideration, by deficiency, will mean difference between parameter distribution number summands sum that compound providing desired accuracy normal approximation. used for solution problem determination separate term provides least possible value guaranteeing prescribed (1−α)-quantile normalized given α∈(0,1). solved condition possess coinciding first three moments. The consideration applied collective risk model order determine insurance payments time Value-at-Risk. also approximation asymptotic independent, identically distributed with accompanying infinitely divisible distribution.