aggregate programsClick on Key links to load the program into the scratch area, where it can be executed to show aggregate statistics and graphics.
Note sev.One is shorthand for a fixed severity of 1. It
can also be specified using the clause sev dhistogram xps [1] [1].
To enter a Tweedie distribution with mean μ and
variance function V(μ) = σ2μp
compute α = (2−p)/(p−1), λ = μ2 − p/((2−p)σ2),
and β = μ1 − p/((p−1)σ2).
Then enter the program agg Tweedie lambda claims sev {1/beta} * gamma {alpha} poisson
where the terms lambda, 1/beta and alpha are replaced by
their computed values.
For an interesting example take μ = 1, p = 1.005 and σ2 = 0.1, producing alpha=199,
beta=2000 (1/beta=0.0005), lambda=10.05025126 and
agg TWEEDIE 10.05025126 claims sev 0.0005 * gamma 199 poisson.
These parameters produce an aggregate that is “close” to a Poisson with a highly multimodal
density. The examples below use p in [1.001, 1.005, 1.01, 1.025, 1.05, 1.1, 1.2, 1.5, 1.9, 1.995].
Once the distributions settle down, look at the probability of zero losses to differentiate between them.
| Program | |
|---|---|
| Key | |
| FreqFixed | agg FreqFixed 10 claims sev sev.One fixed |
| FreqPoisson | agg FreqPoisson 10 claims sev sev.One poisson |
| FreqBernoulli | agg FreqBernoulli .8 claims sev sev.One bernoulli |
| FreqBinomial | agg FreqBinomial 10 claims sev sev.One binomial 0.5 |
| FreqGeometric | agg FreqBinomial 10 claims sev sev.One geometric |
| FreqPascal | agg FreqPascal 10 claims sev sev.One pascal .8 3 |
| FreqNegBin | agg FreqNegBin 10 claims sev sev.One (mixed gamma 0.65) |
| FreqDelaporte | agg FreqDelaporte 10 claims sev sev.One mixed delaporte .65 .25 |
| FreqIG | agg FreqIG 10 claims sev sev.One mixed ig .65 |
| FreqIG | agg FreqIG 10 claims sev sev.One mixed sig 0.5 0.4 |
| FreqSichel | agg FreqSichel 10 claims sev sev.One mixed delaporte .65 -0.25 |
| FreqSichel.gamma | agg FreqSichel.gamma 10 claims sev sev.One mixed sichel.gamma .65 .25 |
| FreqSichel.ig | agg FreqSichel.ig 10 claims sev sev.One mixed sichel.ig .65 .25 |
| FreqBeta | agg FreqBeta 10 claims sev sev.One mixed beta .5 4 |
| Sev0 | agg Sev0 1 claim sev lognorm 10 cv .09 fixed |
| Sev1 | agg Sev1 1 claim sev 10 * lognorm 10 cv .09 fixed |
| Sev2 | agg Sev2 1 claim sev lognorm 10 cv .09 + 20 fixed |
| Sev3 | agg Sev3 1 claim sev 10 * lognorm 10 cv .09 + 20 fixed |
| Sev4 | agg Sev4 1 claim sev 9.559974818331 * lognorm .3 fixed |
| Sev5 | agg Sev5 1 claim sev 9.559974818331 * lognorm .3 + 5 fixed |
| Sev6 | agg Sev6 1 claim sev 10 * lognorm 0.5 cv .3 fixed |
| Sev7 | agg Sev7 1 claim sev 10 * lognorm 1 cv .5 + 5 fixed |
| Sev8 | agg Sev8 1 claim sev 10 * gamma 0.3 fixed |
| Sev9 | agg Sev9 1 claim sev 10 * gamma 1 cv .3 + 5 fixed |
| Sev10 | agg Sev10 1 claim sev 10 * pareto 2.6 - 10 fixed |
| Sev11 | agg Sev11 1 claim sev 2 * uniform 5 + 2.5 fixed |
| Sev12 | agg Sev12 1 claim 130 x 20 sev lognorm 20 cv 0.75 fixed |
| Sev13 | agg Sev13 1 claim 130 x 20 sev 20 * lognorm 0.75 fixed |
| Sev14 | agg Sev14 1 claim 130 x 20 sev 20 * lognorm 1 cv 0.75 fixed |
| Sev15 | agg Sev15 1 claim (130 x 20) sev 20 * lognorm 1 cv 0.75 + 20 fixed |
| Sev16 | agg Sev16: 1 claim sev 50 * beta 3 2 + 10 fixed |
| Sev17 | agg Sev17: 1 claim sev 100 * expon + 10 fixed |
| Sev18 | agg Sev18: 1 claim sev 10 * norm + 50 fixed |
| Sev19 | agg Sev19: 1 claim sev 1 * invgamma 4.07 fixed |
| Sev20 | agg Sev20: 1 claim sev invgauss 10 cv .5 fixed |
| Example1 | agg Example1 10 claims 30 xs 0 sev lognorm 10 cv 0.8 fixed |
| Example2 | agg Example2 10 claims 30 xs 0 sev lognorm 10 cv 0.8 poisson |
| Example3 | agg Example3 10 claims 30 xs 0 sev lognorm 10 cv 0.8 mixed gamma 0.3 |
| Example4 | agg Example4 10 claims 30 xs 0 sev lognorm 10 cv 0.8 mixed delaporte 0.3 0.25 |
| Example5 | agg Example5 10 claims 100 xs 10 sev lognorm 10 cv 0.8 poisson |
| Example6 | agg Example6 10 claims inf xs 10 sev lognorm 10 cv 0.8 poisson |
| Example7 | agg Example7 0.25 claims sev 4 * expon poisson |
| Example8 | agg Example8 0.05 claims sev 20 * expon poisson |
| Example9 | agg Example9 0.05 claims sev 100 * expon poisson |
| Tweedie0 | agg Tweedie0 10.01001 claims sev 0.0001 * gamma 999 poisson |
| Tweedie1 | agg Tweedie1 10.050251 claims sev 0.0005 * gamma 199 poisson |
| Tweedie2 | agg Tweedie2 10.10101 claims sev 0.001 * gamma 99 poisson |
| Tweedie3 | agg Tweedie3 10.25641 claims sev 0.0025 * gamma 39 poisson |
| Tweedie4 | agg Tweedie4 10.526316 claims sev 0.005 * gamma 19 poisson |
| Tweedie5 | agg Tweedie5 11.111111 claims sev 0.01 * gamma 9 poisson |
| Tweedie6 | agg Tweedie6 12.5 claims sev 0.02 * gamma 4 poisson |
| Tweedie7 | agg Tweedie7 20 claims sev 0.05 * gamma 1 poisson |
| Tweedie8 | agg Tweedie8 100 claims sev 0.09 * gamma 0.11111111 poisson |
| Tweedie9 | agg Tweedie9 2000 claims sev 0.0995 * gamma 0.0050251256 poisson |
| ExampleGup | agg ExampleGup 10 claims 100 x 0 sev lognorm 15 cv 0.8 poisson |
| ExampleRet | agg ExampleRet 10 claims 40 xs 10 sev lognorm 15 cv 0.8 poisson |
| ExampleXoL | agg ExampleXoL 10 claims 60 xs 40 sev lognorm 15 cv 0.8 poisson |
| ExampleXoLUC | agg ExampleXoLUC 10 claims 60 xs 40 sev lognorm 15 cv 0.8 ! poisson |
| Example2Gup | agg Example2Gup 10 claims inf x 0 sev lognorm 25 cv 1.0 poisson |
| Example2Ret | agg Example2Ret 10 claims 100 xs 10 sev lognorm 25 cv 1.0 poisson |
| Example2XoL | agg Example2XoL 10 claims inf xs 100 sev lognorm 25 cv 1.0 poisson |
| Example2XoLUC | agg Example2XoLUC 10 claims inf xs 100 sev lognorm 25 cv 1.0 ! poisson |
| MixedLine1 | agg MixedLine1: 1 claim 50 xs 0 sev lognorm 10 cv [0.2, 0.4, 0.6, 0.8, 1.0] wts=5 fixed |
| MixedLine3 | agg MixedLine3: 1 claim 50 xs 0 sev lognorm 10 cv [0.2, 0.4, 0.6, 0.8, 1.0] wt [.2, .3, .3, .15, .05] fixed |
| MixedLine4 | agg MixedLine4: 1 claim 50 xs 0 sev lognorm 10 cv [0.2, 0.4, 0.6, 0.8, 1.0] fixed |
| MixedLine5 | agg MixedLine5: 1 claim 50 xs 0 sev lognorm [10, 15, 20, 25, 50] cv [0.2, 0.4, 0.6, 0.8, 1.0] wts=5 fixed |
| MixedLine6 | agg MixedLine6: 50 claims sev lognorm 12 cv [.75 1 .25] wt [.3 .5 .2] mixed gamma 0.4 |
| MixedLine7 | agg MixedLine7 1 claim sev 100 * beta [1 200 500 100] [100 800 500 1] wt=4 + 10 fixed |
| LimitProfile1 | agg LimitProfile1: 1 claim [1, 5, 10, 20] xs 0 sev lognorm 10 cv 1.2 wt [.50, .20, .20, .1] fixed |
| LimitProfile2 | agg LimitProfile2: 5 claim [10 20 50 100] xs 10 sev lognorm 10 cv 1.2 wt [.50, .20, .20, .1] fixed |
| LimitProfile3 | agg LimitProfile3: [10 10 10 10] claims [inf 10 inf 10] xs [0 0 5 5] sev lognorm 10 cv 1.25 fixed |
| LimitProfile4 | agg LimitProfile4: 1 claim sev lognorm [5 10 15 20] cv .02 wts=4 fixed |
| LimitProfile5 | agg LimitProfile5: 1 claim sev lognorm [5 10 15 20] cv .02 wts=4 fixed |
| LimitProfile6 | agg LimitProfile6: [10 30 15 5] claims [inf 10 inf 10] xs [0 0 5 5] sev lognorm 10 cv [1.0, 1.25, 1.5] wts=3 fixed |
| LimitProfile7 | agg LimitProfile7 [10 20 30] claims [100 200 75] xs [0 50 75] sev lognorm 100 cv [1 2] wts [.6 .4] mixed gamma 0.4 |
| LimitProfile8 | agg LimitProfile8 [10 30] claims sev lognorm 100 cv [1 2] mixed gamma 0.4 |
| CA | agg CA 500 prem at .5 lr 15 x 12 sev gamma 12 cv [2 3 4] wt [.3 .5 .2] mixed gamma 0.4 |
| FL | agg FL 1.7 claims 100 x 5 sev 10 * pareto 1.3 - 10 poisson |
| NY | agg NY 500 prem at .5 lr 15 x 12 sev [20 30 40 10] * gamma [9 10 11 12] cv [1 2 3 4] wt=4 mixed gamma 0.4 |
| Blend0 | agg Blend0 1 claim sev lognorm 12 cv [0.1, 0.3, 0.5] wts=3 fixed |
| Blend1 | agg Blend1 1 claim sev lognorm 12 cv [0.1, 0.3, 0.5] fixed |
| Blend2 | agg Blend2 10 claims [5 10 15] x 0 sev lognorm 12 cv [1, 1.5, 3] fixed |
| Blend3 | agg Blend3 10 claims [5 10 15] x 0 sev lognorm 12 cv [1, 1.5, 3] wt=3 fixed |
| logo1 | agg logo1 0.05 claim [10, 22.632, 35.263, 47.895, 60.526, 73.158, 85.789, 98.421, 111.05, 123.68, 136.32, 148.95, 161.58, 174.21, 186.84, 199.47, 212.11, 224.74, 237.37, 250] xs 0 sev lognorm 100 cv 1 fixed |
| logo2 | agg logo2 1 claim [10, 22.632, 35.263, 47.895, 60.526, 73.158, 85.789, 98.421, 111.05, 123.68, 136.32, 148.95, 161.58, 174.21, 186.84, 199.47, 212.11, 224.74, 237.37, 250] xs 0 sev lognorm 100 cv 1 fixed |
| dHist1 | agg dHist1 1 claim sev dhistogram xps [1, 10, 40] [.5, .3, .2] fixed |
| cHist1 | agg cHist1 1 claim sev chistogram xps [1, 10, 40] [.5, .3, .2] fixed |
| dHist2 | agg dHist2 1 claim sev dhistogram xps [1, 2, 5, 100] [.5, .25, 0.2, 0.05] fixed |
| dHist3 | agg dHist3 10 claim sev dhistogram xps [1, 2, 5, 100] [.5, .25, 0.2, 0.05] fixed |
| dHist4 | agg dHist4 10 claim sev dhistogram xps [1, 2, 5, 100] [.5, .25, 0.2, 0.05] poisson |
| BodoffWind | agg wind 1 claim sev dhistogram xps [0, 99] [0.80, 0.20] fixed |
| BodoffQuake | agg quake 1 claim sev dhistogram xps [0, 100] [0.95, 0.05] fixed |
| Bodoff2Wind | agg wind 1 claim sev dhistogram xps [0, 50] [0.80, 0.20] fixed |
| Bodoff2Quake | agg quake 1 claim sev dhistogram xps [0, 100] [0.95, 0.05] fixed |
| Bodoff3Wind | agg wind 1 claim sev dhistogram xps [0, 5] [0.80, 0.20] fixed |
| Bodoff3Quake | agg quake 1 claim sev dhistogram xps [0, 100] [0.95, 0.05] fixed |