Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: insurance
See also: INSgam INSlogn INSpareto INSbur

Quantlet: INSwei
Description: returns the pure risk premium for Weibull distribution of losses.

Reference(s):

Usage: y = INSwei(b,d2,d1,c,m2,m1,alpha,beta,ind)
Input:
b n x 1 vector, deductible (in case of fixed deductible, franchise deductible or proportional deductible)
d2 n x 1 vector, maximum amount, d2>d1, of linear reduction for disappearing deductible
d1 scalar, minimum amount of linear reduction for disappearing deductible
c scalar, deductible (in case of limited proportional deductible)
m2 n x 1 vector, maximum amount, m2>m1, for limited proportional deductible
m1 scalar, minimum amount for limited proportional deductible
alpha scalar, parameter alpha from Weibull distribution
beta scalar, parameter beta from Weibull distribution
ind scalar, if ind=1, franchise deductible if ind=2, fixed amount deductible if ind=3, proportional deductible if ind=4, limited proportional deductible if ind=5, disappearing deductible
Output:
y n x 1 vector, value of pure risk premium for Weibull distribution of losses

Example:
library("insurance")
library("distribs")
library("plot")
alpha=0.4525                   ;alpha parameter in Weibull distribution
beta=6.8915*(10^5)             ;beta parameter in Weibull distribution
a=(0:100)*1000000              ;argument in payment functions
u1=INSwei(a,0,0,0,0,0,alpha,beta,1)
u2=INSwei(a,0,0,0,0,0,alpha,beta,2)
scal=1000000
d1=setmask(a/scal~u1/scal,"line","black")
d2=setmask(a/scal~u2/scal,"line","red")
disp=createdisplay(1,1)
show(disp,1,1,d1,d2)
setgopt(disp,1,1,"xmajor",50,"ymajor",0.5)
setgopt(disp,1,1,"yvalue",0|1)
setgopt(disp,1,1,"xvalue",0|1)
setgopt(disp,1,1, "xlabel", "Deductible(USD million)", "ylabel", " Premium(USD million)")
setgopt(disp,1,1,"border",0)
setgopt(disp,1,1,"title","Pure Risk Premium - Weibull")

Result:
Plot of pure risk premium under franchise deductible (black)
and fixed amount deductible (red).
Example:
library("insurance")
library("distribs")
library("plot")
alpha=0.4525                        ;alpha parameter in Weibull distribution
beta=6.8915*(10^5)                  ;beta parameter in Weibull distribution
m2=(10:100)*1000000                   ;argument in payment functions
c1=0.2                              ;parameters c and m1 in the case of limited proportional deductible
c2=0.4
m11=1000000
m12=500000
u1=INSwei(0,0,0,c1,m2,m11,alpha,beta,4)
u2=INSwei(0,0,0,c2,m2,m11,alpha,beta,4)
u3=INSwei(0,0,0,c1,m2,m12,alpha,beta,4)
u4=INSwei(0,0,0,c2,m2,m12,alpha,beta,4)
scal=1000000
d1=setmask(m2/scal~u1/scal,"line","black")
d2=setmask(m2/scal~u2/scal,"line","red")
d3=setmask(m2/scal~u3/scal,"line","green")
d4=setmask(m2/scal~u4/scal,"line","blue")
disp=createdisplay(1,1)
show(disp,1,1,d1,d2,d3,d4)
setgopt(disp,1,1,"xmajor",50,"ymajor",0.5)
setgopt(disp,1,1,"yvalue",0|1)
setgopt(disp,1,1,"xvalue",0|1)
setgopt(disp,1,1, "xlabel", "Deductible(USD million)", "ylabel", " Premium(USD million)")
setgopt(disp,1,1,"border",0)
setgopt(disp,1,1,"title","Pure Risk Premium - Weibull")

Result:
Plots of pure risk premium under limited proportional deductible for parameters c1,m11 (black), c2,m11 (red),
c1,m12 (green) and c2,m12 (blue).



Author: A. Wylomanska, 20031205 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006