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; 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. |
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.
An object of mode "function"
with the same arguments as
pdf
or cdf
, except "lower.tail"
,
"log.p"
and "log"
, which are not supported.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, Panjer & Willmot, Loss Models, Second Edition, Wiley, 2004.
## 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)