Loglogistic | 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 |
shape, scale |
parameters. Must be strictly positive. |
rate |
an alternative way to specify the scale. |
log, log.p |
logical; if |
lower.tail |
logical; if |
order |
order of the moment. |
limit |
limit of the loss variable. |
The loglogistic distribution with parameters shape
=
\gamma
and scale
= \theta
has density:
f(x) = \frac{\gamma (x/\theta)^\gamma}{%
x [1 + (x/\theta)^\gamma]^2}
for x > 0
, \gamma > 0
and \theta > 0
.
The k
th raw moment of the random variable X
is
E[X^k]
, -\gamma < k < \gamma
.
The k
th limited moment at some limit d
is E[\min(X,
d)^k]
, k > -\gamma
and 1 - k/\gamma
not a negative integer.
dllogis
gives the density,
pllogis
gives the distribution function,
qllogis
gives the quantile function,
rllogis
generates random deviates,
mllogis
gives the k
th raw moment, and
levllogis
gives the k
th moment of the limited loss
variable.
Invalid arguments will result in return value NaN
, with a warning.
levllogis
computes the limited expected value using
betaint
.
Also known as the Fisk distribution. See also Kleiber and Kotz (2003) for alternative names and parametrizations.
The "distributions"
package vignette provides the
interrelations between the continuous size distributions in
actuar and the complete formulas underlying the above functions.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
Kleiber, C. and Kotz, S. (2003), Statistical Size Distributions in Economics and Actuarial Sciences, Wiley.
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.
dpareto3
for an equivalent distribution with a location
parameter.
exp(dllogis(2, 3, 4, log = TRUE))
p <- (1:10)/10
pllogis(qllogis(p, 2, 3), 2, 3)
## mean
mllogis(1, 2, 3)
## case with 1 - order/shape > 0
levllogis(10, 2, 3, order = 1)
## case with 1 - order/shape < 0
levllogis(10, 2/3, 3, order = 1)
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