In: Statistics and Probability
An insurance policy has an ordinary deductible of 100 and a
maximum covered loss of 10,000. You observe the following six
payments:
100 200 500 600 1000 5000
In addition, there are three payments at the limit. You fit a single
parameter Pareto distribution with θ = 50 to the ground up
distribution using maximum likelihood. Determine the estimated
parameterα.
Xi | log Xi | log (Xi /Ɵ) |
100 | 4.605 | 0.0921 |
200 | 5.298 | 0.1060 |
500 | 6.215 | 0.1243 |
600 | 6.397 | 0.1279 |
1000 | 6.908 | 0.1382 |
5000 | 8.517 | 0.1703 |
Sum | 37.940 | 0.7588 |