Density function, distribution function, quantile function, random generation
raw moments and limited moments for the Inverse Pareto distribution
with parameters shape and scale.
dinvpareto(x, shape, scale, log = FALSE)
pinvpareto(q, shape, scale, lower.tail = TRUE, log.p = FALSE)
qinvpareto(p, shape, scale, lower.tail = TRUE, log.p = FALSE)
rinvpareto(n, shape, scale)
minvpareto(order, shape, scale)
levinvpareto(limit, shape, scale, order = 1)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.
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.
dinvpareto gives the density,
pinvpareto gives the distribution function,
qinvpareto gives the quantile function,
rinvpareto generates random deviates,
minvpareto gives the \(k\)th raw moment, and
levinvpareto calculates the \(k\)th limited moment.
Invalid arguments will result in return value NaN, with a warning.
The inverse Pareto distribution with parameters shape \(=
\tau\) and scale \(= \theta\) has density:
$$f(x) = \frac{\tau \theta x^{\tau - 1}}{%
(x + \theta)^{\tau + 1}}$$
for \(x > 0\), \(\tau > 0\) and \(\theta > 0\).
The \(k\)th raw moment of the random variable \(X\) is \(E[X^k]\), \(-\tau < k < 1\).
The \(k\)th limited moment at some limit \(d\) is \(E[\min(X, d)^k]\), \(k > -\tau\).
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.
# NOT RUN {
exp(dinvpareto(2, 3, 4, log = TRUE))
p <- (1:10)/10
pinvpareto(qinvpareto(p, 2, 3), 2, 3)
minvpareto(0.5, 1, 2)
# }
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