# coverage: Density and Cumulative Distribution Function for Modified... In actuar: Actuarial Functions and Heavy Tailed Distributions

 coverage R Documentation

## 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.

### 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.

### 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.

### Note

Setting arguments of the function returned by `coverage` using `formals` may very well not work as expected.

### Author(s)

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

### References

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

`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)

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)
``````

actuar documentation built on Nov. 8, 2023, 9:06 a.m.