Stochastic processes - claim arrival process

Hey guys! I am working with stochastic processes and came round the flowing problem:

are iid and is such independent random variable that . What is the distribution of .

Well, I have tried to calculate expected value of first and then has the distribution equal to convolved times. Bot this somehow doesn't feel right. However, this looks awfully similar to compound Poison process but claim arrival times are not Poison distributed... Could anyone give a hint on this problem?