nlirms (version 3.4.4)

rmspfc: Rate-making system based on the posteriori freuency component

Description

rmspfc() function gives the rate-making system based on the posteriori freuency component. Values given by rmspfc() function is equal to with expected number of claims given by enc.family (i.e. enc.PGA, enc.PIGA, enc.PGIG) for different amounts of time and claim.

Usage

rmspfc(time = 5, claim = 5, fmu = .2, fsigma = 2, fnu = 1,
  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

fmu

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

fsigma

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

fnu

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

family

a nlirms.family object, which is used to define the frequency 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

rmspfc() function return the expected number 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 time and claim. for example the cell with time=2 and claim=1, shows the expected number of claims in next year for a ploicyholder that who had a one claim in past two years.

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 Poisson-Gamma model for frequency component
rmspfc(time = 5, claim = 5, fmu = .2, fsigma = 2, fnu = 1, family = "PGA", round
= 2, size = 8, padlength = 4, padwidth = 2)

# rate-Making system based on the Poisson-Inverse Gamma model for frequency component
rmspfc(time = 5, claim = 5, fmu = .2, fsigma = 2, fnu = 1, family = "PIGA",
round = 2, size = 8, padlength = 4, padwidth = 2)

# rate-Making system based on the Poisson-Generalized Inverse Gaussian model for frequency
rmspfc(time = 5, claim = 5, fmu = .2, fsigma = 2, fnu = 1, family = "PGIG",
round = 2, size = 8, padlength = 4, padwidth = 2)
# }