coverage {actuar}R Documentation

Density and Cumulative Distribution Function for Modified Data

Description

Compute probability density 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(dist, deductible = 0, franchise = FALSE,
         limit = Inf, coinsurance = 1, inflation = 0,
         per.loss = FALSE, cdf = FALSE)

Arguments

dist character string of the name 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.
cdf logical; TRUE for the cumulative distribution function, FALSE (default) for the probability distribution function.

Details

coverage() returns the pdf or cdf of distribution dist under coverage modifications. Functions pdist and, if cdf = FALSE, ddist must exist.

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

Value

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

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

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("gamma", deductible = 1)

## Add a limit
f <- coverage("gamma", 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(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), lty = 2, add = TRUE) # modified
points(6, f(6, 3, 1), type = "h", pch = 16)
points(6, f(6, 3, 1), pch = 16)

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

[Package actuar version 0.9-2 Index]