Model claim frequencies using Poisson processes.

Free CAS MAS-I (Modern Actuarial Statistics I) lesson in Probability Models. 11 min read, ~1,698 words.

Homogeneous Poisson process with rate: with independent stationary increments, and mean and variance both equal to. Inter-arrival times are iid with mean; the memoryless property means past waiting carries no information about future waiting. Waiting time to the -th claim is with mean. Superposition: the sum of independent Poisson processes...