| InverseParalogistic {actuar} | R Documentation |
Density function, distribution function, quantile function, random generation,
raw moments and limited moments for the Inverse Paralogistic
distribution with parameters shape and scale.
dinvparalogis(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pinvparalogis(q, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
qinvparalogis(p, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
rinvparalogis(n, shape, rate = 1, scale = 1/rate)
minvparalogis(order, shape, rate = 1, scale = 1/rate)
levinvparalogis(limit, shape, rate = 1, scale = 1/rate,
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, scale |
parameters. Must be strictly positive. |
rate |
an alternative way to specify the scale. |
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 Inverse Paralogistic distribution with parameters shape
= a and scale = s has density:
f(x) = a^2 (x/s)^(a^2)/(x [1 + (x/s)^a]^(a + 1))
for x > 0, a > 0 and b > 0.
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].
dinvparalogis gives the density,
pinvparalogis gives the distribution function,
qinvparalogis gives the quantile function,
rinvparalogis generates random deviates,
minvparalogis gives the kth raw moment, and
levinvparalogis 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(dinvparalogis(2, 3, 4, log = TRUE)) p <- (1:10)/10 pinvparalogis(qinvparalogis(p, 2, 3), 2, 3) minvparalogis(-1, 2, 2) levinvparalogis(10, 2, 2, order = 1)