actuar (version 3.3-4)

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)

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.

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.

Author

Vincent Goulet and Mathieu Pigeon

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 pdf is specified, the pdf is returned; if pdf is missing or NULL, the cdf is returned. Note that cdf is needed if there is a deductible or a limit.

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

See Also

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

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)

## Coinsurance alone; only case that does not require the cdf
coverage(dgamma, coinsurance = 0.8)