Estimation, Evaluation, and Selection of Actuarial Models
Estimation, Evaluation, and Selection of Actuarial Models
Estimation, Evaluation, and Selection of Actuarial Models
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101<br />
f(x)<br />
1<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
0 1 2 3 4 5 6<br />
x<br />
Triangular kernel for Exercise 13<br />
This is clearly not satisfactory. The gamma kernel is not available because there would be<br />
positive probability at values greater than 5. Your author tried to solve this by using the beta<br />
distribution (see LMA). With θ knowntobe5,themean(tobesetequaltoy) is5a/(a + b). In<br />
order to have some smoothing control <strong>and</strong> to determine parameter values, the sum a + b was fixed.<br />
In the following graph, a value <strong>of</strong> 50 was used for the sum. The kernel is<br />
k y (x) =<br />
Γ(50)<br />
³ x<br />
´10y ³<br />
1 − x ´50−10y−1 1<br />
Γ(10y)Γ(50 − 10y) 5 5 x , 0
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