esc.EIGA() function gives the expected severity of next claim for a policyholder with regards to the claims severity and freuency history of this policyholder in past time, based on the Exponential-Inverse Gamma (Pareto) model.
EIGA(x, mu, sigma)
dEIGA(x= 100, claim=1, mu = 50, sigma = 2)
esc.EIGA(sumsev=100, claim =1, mu =50 , sigma = 2)vector of quantiles
positive mean parameter of the Exponential-Inverse Gamma (Pareto) distribution that it wil be obtained from fitting Exponential-Inverse Gamma (Pareto) distribution to the claim severity data.
positive scale parameter of the Exponential-Inverse Gamma (Pareto) distribution that it will be obtained from fitting Exponential-Inverse Gamma (Pareto) distribution to the claim severity data.
sum severity of all claims that a policyholder had in past years
total number of claims that a policyholder had in past years
esc.EIGA() function return the expected severity of next claim based on the Exponential-Inverse Gamma (Pareto) model. dEIGA() function return the probability density of Exponential-Inverse Gamma (Pareto) distribution.
Consider that x be the size of the claim of each insured and z is the mean claim size for each insured, where conditional distribution of the size given the parameter z, is distributed according to exponential(z). if z following the Inverse Gamma distribution, z~IGA(mu, sigma), with Parameterization that E(z)=mu, Then by apply the Bayes theorem the unconditional distribution of claim size x will be exponential-Inverse Gamma (Pareto) model, EIGA~(mu, sigma), with probability density function as the following form:
f(x)=sigma*[(mu*(sigma-1))^sigma]/[(x+mu*(sigma-1))^(sigma+1)]
let claim=k1+ ...+kt, is the total number of claims and sumsev=x1+ ...+xclaim is the total amuont of claim size where xi is the amount of claim size in the claim i, (i=1, ..., i=claim). by apply the Bayes theorem, the posterior structure function of x given the claims size history of the policyholder i.e. f(x|x1, ..., xclaim), following the Inverse Gamma distribution, IGA(claim+sigma, sumsev*mu*(sigma-1). the expected claim severity based on the EIGA model is equal to the mean of this posteriori distribution.
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# NOT RUN {
esc.EIGA(sumsev=100 ,claim=1 , mu=50, sigma=2)
claim=0:5
esc.EIGA(sumsev=100 ,claim=claim , mu=50, sigma=2)
# }
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