Using R

Aggregate claims S follow a compound distribution where the number of claims N follows a (type 2) negative binomial distribution with parameters k = 10 and p=0.1. Individual claim sizes X follow a lognormal distribution with parameters u = 10 and o? = 5. (i) Simulate 10,000 random variates from the compound distribution and display the first five values of your data. (Use seed value 16.) Compare the sample mean and variance of your dataset to the population mean and variance of S. Hint: Use the formula for E(s) and Var(s) given on page 16 of the Tables. Adjust your answer to part (i) to simulate the insurers aggregate claims net of reinsurance, Sj, if an individual excess of loss arrangement applies, with retention limit M=2,000,000