Statistical analysis of compound distributions

The probability distribution of a random variable created by summing a random number of the independent and identically distributed random variables is called a compound probability distribution. In this work is described a compound distribution as well as a calculation of its characteristics. Especially, the thesis is focused on studying a special case of compound distribution where each addend has the log-normal distribution and their number has the negative binomial distribution. Here are also described some approaches to estimate the parameters of LN and NB distribution. Further, the impact of these estimates on the final compound distribution is analyzed