| Loglogistic {actuar} | R Documentation |
Density function, distribution function, quantile function, random generation,
raw moments and limited moments for the Loglogistic distribution with
parameters shape and scale.
dllogis(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pllogis(q, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
qllogis(p, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
rllogis(n, shape, rate = 1, scale = 1/rate)
mllogis(order, shape, rate = 1, scale = 1/rate)
levllogis(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 Loglogistic distribution with parameters shape = a and scale = s has density:
f(x) = a (x/s)^a / (x [1 + (x/s)^a]^2)
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].
dllogis gives the density,
pllogis gives the distribution function,
qllogis gives the quantile function,
rllogis generates random deviates,
mllogis gives the kth raw moment, and
levllogis gives the kth moment of the limited loss
variable.
Invalid arguments will result in return value NaN, with a warning.
Also known as the Fisk distribution.
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(dllogis(2, 3, 4, log = TRUE)) p <- (1:10)/10 pllogis(qllogis(p, 2, 3), 2, 3) mllogis(1, 2, 3) levllogis(10, 2, 3, order = 1)