nlirms (version 3.4.4)

rmspsc: Rate-making system based on the posteriori severity component

Description

rmspsc() function gives the rate-making system based on the posteriori severity component. Values given by rmspsc() function is equal to with expected severity of claims given by esc.family (i.e. esc.EGA, esc.EIGA, esc.EGIG) for different amounts of claimS.

Usage

rmspsc(time=5, claim=5, sumsev=100, smu = 50, ssigma = 3, snu = 2,
family ="NO", round=2, size=8 , padlength=4, padwidth=2, ...)

Arguments

time

time period to designing of rate-making system based on the posteriori freuency component

claim

number of claims to designing of rate-making system based on the posteriori freuency component

sumsev

sum severity of all claims to designing of rate-making system based on the posteriori freuency component

smu

mu parameter of severity model in designing of rate-making system

ssigma

sigma parameter of severity model in designing of rate-making system

snu

nu parameter of severity model in designing of rate-making system

family

a nlirms.family object, which is used to define the severity model to designing of rate-making system

round

rounds the rate-making system values to the specified number of decimal places

size

indicates the size of graphical table for rate-making system

padlength

indicates the length of each graphical table cells

padwidth

indicates the width of each graphical table cells

...

for further arguments

Value

rmspsc() function return the expected severity of claims of policyholders based on the different models.

Details

rmspfc() function gives the rate-making system in the form of a table where each table cells is related to the one claim. for example if sumsev=100, then the cell with claim=2, shows the expected severity of claims in next year for a ploicyholder that who had a two claim in past years in which the total size of two claim was equal to 100. Rate-Making system based on the severity component does not dependent to the time.

References

Frangos, N. E., & Vrontos, S. D. (2001). Design of optimal bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin: The Journal of the IAA, 31(1), 1-22.

Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance, Kluwer Academic Publishers, Massachusetts.

MohammadPour, S., Saeedi, K., & Mahmoudvand, R. (2017). Bonus-Malus System Using Finite Mixture Models. Statistics, Optimization & Information Computing, 5(3), 179-187.

Najafabadi, A. T. P., & MohammadPour, S. (2017). A k-Inflated Negative Binomial Mixture Regression Model: Application to Rate--Making Systems. Asia-Pacific Journal of Risk and Insurance, 12.

Rigby, R. A., & Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54(3), 507-554.

Stasinopoulos, D. M., Rigby, B. A., Akantziliotou, C., Heller, G., Ospina, R., & Motpan, N. (2010). gamlss. dist: Distributions to Be Used for GAMLSS Modelling. R package version, 4-0.

Stasinopoulos, D. M., & Rigby, R. A. (2007). Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, 23(7), 1-46.

Examples

# NOT RUN {
# rate-making system based on the Exponential-Gamma model for severity component
rmspsc(time=5, claim=5, sumsev=100, smu = 50, ssigma = 3, snu = 2, family
="EGA", round=2, size=8 , padlength=4, padwidth=2)

# rate-making system based on the Exponential-Inverse Gamma model for severity component
rmspsc(time=5, claim=5, sumsev=100, smu = 50, ssigma = 3, snu = 2, family
="EIGA", round=2, size=8 , padlength=4, padwidth=2)

# rate-making system based on the Exponential-Generalized Inverse Gaussian model for severity
rmspsc(time=5, claim=5, sumsev=100, smu = 50, ssigma = 3, snu = 2, family
="EGIG", round=2, size=8 , padlength=4, padwidth=2)
# }