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Density function, distribution function, quantile function, random generation,
raw moments, and limited moments for the Inverse Gamma distribution
with parameters shape
and scale
.
dinvgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pinvgamma(q, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
qinvgamma(p, shape, rate = 1, scale = 1/rate,
lower.tail = TRUE, log.p = FALSE)
rinvgamma(n, shape, rate = 1, scale = 1/rate)
minvgamma(order, shape, rate = 1, scale = 1/rate)
levinvgamma(limit, shape, rate = 1, scale = 1/rate,
order = 1)
mgfinvgamma(t, shape, rate =1, scale = 1/rate, log =FALSE)
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
logical; if TRUE
(default), probabilities are
order of the moment.
limit of the loss variable.
numeric vector.
dinvgamma
gives the density,
pinvgamma
gives the distribution function,
qinvgamma
gives the quantile function,
rinvgamma
generates random deviates,
minvgamma
gives the levinvgamma
gives the mgfinvgamma
gives the moment generating function in t
.
Invalid arguments will result in return value NaN
, with a warning.
The inverse gamma distribution with parameters shape
scale
gamma()
and defined in its help.)
The special case shape == 1
is an
Inverse Exponential distribution.
The
The moment generating function is given by
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.
# NOT RUN {
exp(dinvgamma(2, 3, 4, log = TRUE))
p <- (1:10)/10
pinvgamma(qinvgamma(p, 2, 3), 2, 3)
minvgamma(-1, 2, 2) ^ 2
levinvgamma(10, 2, 2, order = 1)
mgfinvgamma(-1, 3, 2)
# }
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