coverage {actuar}  R Documentation 
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.
coverage(pdf, cdf, deductible = 0, franchise = FALSE, limit = Inf, coinsurance = 1, inflation = 0, per.loss = FALSE)
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; 
limit 
a unique positive numeric value larger than

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; 
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.
An object of mode "function"
with the same arguments as
pdf
or cdf
, except "lower.tail"
,
"log.p"
and "log"
, which are not supported.
Setting arguments of the function returned by coverage
using
formals
may very well not work as expected.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
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.
## 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)