Density and Cumulative Distribution Function for Modified Data
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.