actuar (version 0.9-4)

coverage: Density and Cumulative Distribution Function for Modified Data

Description

Compute probability density function or cumulative distribution function of the payment per payment or payment per loss random variable under any combination of the following coverage modifications: deductible, limit, coinsurance, inflation.

Usage

coverage(pdf, cdf, deductible = 0, franchise = FALSE,
         limit = Inf, coinsurance = 1, inflation = 0,
         per.loss = FALSE)

Arguments

pdf, cdf

function object or character string naming a function to compute, respectively, the probability density function and cumulative distribution function of a probability law.

deductible

a unique positive numeric value.

franchise

logical; TRUE for a franchise deductible, FALSE (default) for an ordinary deductible.

limit

a unique positive numeric value larger than deductible.

coinsurance

a unique value between 0 and 1; the proportion of coinsurance.

inflation

a unique value between 0 and 1; the rate of inflation.

per.loss

logical; TRUE for the per loss distribution, FALSE (default) for the per payment distribution.

Value

• An object of mode "function" with the same arguments as pdf or cdf, except "lower.tail", "log.p" and "log", which are not supported.

Details

coverage() returns a function to compute the probability density function (pdf) or the cumulative distribution function (cdf) of the distribution of losses under coverage modifications. The pdf and cdf of unmodified losses are pdf and cdf, respectively.

If both pdf and cdf are specified, the pdf is returned; if pdf is missing or NULL, the cdf is returned. Hence, cdf must always be specified.

See vignette("coverage") for the exact definitions of the per payment and per loss random variables under an ordinary or franchise deductible.

References

Klugman, Panjer & Willmot, Loss Models, Second Edition, Wiley, 2004.

Examples

## Default case: pdf of the per payment random variable with
## an ordinary deductible
coverage(dgamma, pgamma, deductible = 1)

## Add a limit
f <- coverage(dgamma, pgamma, deductible = 1, limit = 7)
f <- coverage("dgamma", "pgamma", deductible = 1, limit = 7) # same
f(0, shape = 3, rate = 1)
f(2, shape = 3, rate = 1)
f(6, shape = 3, rate = 1)
f(8, shape = 3, rate = 1)
curve(dgamma(x, 3, 1), xlim = c(0, 10), ylim = c(0, 0.3))    # original
curve(f(x, 3, 1), xlim = c(0.01, 5.99), col = 4, add = TRUE) # modified
points(6, f(6, 3, 1), pch = 21, bg = 4)

## Cumulative distribution function
F <- coverage(cdf = pgamma, deductible = 1, limit = 7)
F(0, shape = 3, rate = 1)
F(2, shape = 3, rate = 1)
F(6, shape = 3, rate = 1)
F(8, shape = 3, rate = 1)
curve(pgamma(x, 3, 1), xlim = c(0, 10), ylim = c(0, 1))    # original
curve(F(x, 3, 1), xlim = c(0, 5.99), col = 4, add = TRUE)  # modified
curve(F(x, 3, 1), xlim = c(6, 10), col = 4, add = TRUE)    # modified

## With no deductible, all distributions below are identical
coverage(dweibull, pweibull, limit = 5)
coverage(dweibull, pweibull, per.loss = TRUE, limit = 5)
coverage(dweibull, pweibull, franchise = TRUE, limit = 5)
coverage(dweibull, pweibull, per.loss = TRUE, franchise = TRUE,
         limit = 5)