| SingleParameterPareto {actuar} | R Documentation |
Density function, distribution function, quantile function, random generation,
raw moments, and limited moments for the Single-parameter Pareto
distribution with parameter shape.
dpareto1(x, shape, min, log = FALSE) ppareto1(q, shape, min, lower.tail = TRUE, log.p = FALSE) qpareto1(p, shape, min, lower.tail = TRUE, log.p = FALSE) rpareto1(n, shape, min) mpareto1(order, shape, min) levpareto1(limit, shape, min, order = 1)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If length(n) > 1, the length
is taken to be the number required. |
shape |
parameter. Must be strictly positive. |
min |
lower bound of the support of the distribution. |
log, log.p |
logical; if TRUE, probabilities/densities
p are returned as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
P[X <= x], otherwise, P[X > x]. |
order |
order of the moment. |
limit |
limit of the loss variable. |
The Single-parameter Pareto distribution with parameter shape
= a has density:
f(x) = a b^a/x^(a + 1)
for x > b, a > 0 and b > 0.
Although there appears to be two parameters, only shape is a true
parameter. The value of min = b must be set in
advance.
The kth raw moment of the random variable X is E[X^k] and the kth limited moment at some limit d is E[min(X, d)^k].
dpareto1 gives the density,
ppareto1 gives the distribution function,
qpareto1 gives the quantile function,
rpareto1 generates random deviates,
mpareto1 gives the kth raw moment, and
levpareto1 gives the kth moment of the limited loss
variable.
Invalid arguments will result in return value NaN, with a warning.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.
exp(dpareto1(5, 3, 4, log = TRUE)) p <- (1:10)/10 ppareto1(qpareto1(p, 2, 3), 2, 3) mpareto1(2, 3, 4) - mpareto(1, 3, 4) ^ 2 levpareto(10, 3, 4, order = 2)