Samples independent realizations of S = X[1] + ... + X[N], drawing frequencies first and then independent severities conditional on those counts. A zero-frequency realization has aggregate loss zero. The model assumes iid severities independent of frequency. Whenever the moments exist, E[S] = E[N] E[X], and Var(S) = E[N] Var(X) + Var(N) E[X]^2.
Arguments
- x
A [collective_risk_spec()] object. Zero-payment specifications produced by [to_payment_basis()] are also accepted.
- n_sim
Positive integer number of independent realizations.
- seed
Optional nonnegative integer random seed, restored after use.
- max_claims
Maximum total number of individual claim draws in one invocation. Exceeding this protective allocation limit is an error, not a truncation of the frequency distribution.
Details
The resulting aggregate distribution follows the frequency and severity specifications on their explicitly declared count basis. All individual severities are iid and independent of frequency.
Examples
model <- collective_risk_spec(frequency_spec("poisson", lambda = 2),
severity_spec("degenerate", value = 100))
simulate_aggregate(model, n_sim = 5, seed = 30)
#> # A tibble: 5 × 3
#> simulation claim_count aggregate_loss
#> <int> <dbl> <dbl>
#> 1 1 0 0
#> 2 2 2 200
#> 3 3 1 100
#> 4 4 2 200
#> 5 5 1 100