The paper considers the asymptotic behavior of the reserve of an organization subjected to risk in the case when the number of factors leading to loss is random. Burr distribution is considered as loss distribution. An asymptotic comparison of the activities of such organizations is carried out in terms of the necessary additional number of such factors (asymptotic deficiency). Two examples illustrating tne obtained results are presented. The first example concerns extreme order statistics, and the second one deals with the truncated Poisson and binomial distributions.
Keywords:
Reserve of insurance company, sample of random size, Burr distribution, asymptotic expansions, truncated Poisson and binomial distributions, extreme order statistics, asymptotic deficiency
