Density function, distribution function, quantile function, random generation,
raw moments and limited moments for the Inverse Weibull distribution
with parameters shape
and scale
.
dinvweibull(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pinvweibull(q, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
qinvweibull(p, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
rinvweibull(n, shape, rate = 1, scale = 1/rate)
minvweibull(order, shape, rate = 1, scale = 1/rate)
levinvweibull(limit, shape, rate = 1, scale = 1/rate,
order = 1)
dinvweibull
gives the density,
pinvweibull
gives the distribution function,
qinvweibull
gives the quantile function,
rinvweibull
generates random deviates,
minvweibull
gives the \(k\)th raw moment, and
levinvweibull
gives the \(k\)th moment of the limited loss
variable.
Invalid arguments will result in return value NaN
, with a warning.
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1
, the length is
taken to be the number required.
parameters. Must be strictly positive.
an alternative way to specify the scale.
logical; if TRUE
, probabilities/densities
\(p\) are returned as \(\log(p)\).
logical; if TRUE
(default), probabilities are
\(P[X \le x]\), otherwise, \(P[X > x]\).
order of the moment.
limit of the loss variable.
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
The inverse Weibull distribution with parameters shape
\(=
\tau\) and scale
\(= \theta\) has density:
$$f(x) = \frac{\tau (\theta/x)^\tau e^{-(\theta/x)^\tau}}{x}$$
for \(x > 0\), \(\tau > 0\) and \(\theta > 0\).
The special case shape == 1
is an
Inverse Exponential distribution.
The \(k\)th raw moment of the random variable \(X\) is \(E[X^k]\), \(k < \tau\), and the \(k\)th limited moment at some limit \(d\) is \(E[\min(X, d)^k]\), all \(k\).
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.
exp(dinvweibull(2, 3, 4, log = TRUE))
p <- (1:10)/10
pinvweibull(qinvweibull(p, 2, 3), 2, 3)
mlgompertz(-1, 3, 3)
levinvweibull(10, 2, 3, order = 1)
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