InversePareto {actuar} | R Documentation |
The Inverse Pareto Distribution
Description
Density function, distribution function, quantile function, random generation
raw moments and limited moments for the Inverse Pareto distribution
with parameters shape
and scale
.
Usage
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)
Arguments
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
shape , scale |
parameters. Must be strictly positive. |
log , log.p |
logical; if |
lower.tail |
logical; if |
order |
order of the moment. |
limit |
limit of the loss variable. |
Details
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
.
Value
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.
Note
Evaluation of levinvpareto
is done using numerical integration.
The "distributions"
package vignette provides the
interrelations between the continuous size distributions in
actuar and the complete formulas underlying the above functions.
Author(s)
Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon
References
Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.
Examples
exp(dinvpareto(2, 3, 4, log = TRUE))
p <- (1:10)/10
pinvpareto(qinvpareto(p, 2, 3), 2, 3)
minvpareto(0.5, 1, 2)