Resumen
The paper presents statistical modeling of some random sum models. Poisson-binomial, Poisson, geometric random sums and random sums with volume of three-point symmetric distribution were modeled and analyzed. The results of this work are relevant not only for insurance business, but also for any other business that involves random accumulation of outcomes. From the nature of distribution of random volume will record the limit distribution of the random amount and the speed of its convergence. Structure of the limit distribution plays an important role in the evaluation of quintiles and testing of hypotheses. The necessary statistical modeling is carried out, which confirms the practical application of asymptotic models. Difference of limit distributions in the class of mixed Poisson sums is underlined. Estimates of the convergence rate of some simulated random sums to their limit distributions are made. To estimate Poisson-binomial, Poisson and mixed Poisson random sums, Berry-Esseen inequality was applied. To estimate quantile of random sum with volume of threepoint symmetric distribution, an asymptotic decomposition of distribution function of non-normalized statistics of random sum was carried out. Calculation of the required reserve of insurance company is to estimate the level quintile close to one.