InverseBurr {actuar}R Documentation

The Inverse Burr Distribution

Description

Density function, distribution function, quantile function, random generation, raw moments and limited moments for the Inverse Burr distribution with parameters shape1, shape2 and scale.

Usage

dinvburr(x, shape1, shape2, rate = 1, scale = 1/rate,
         log = FALSE)
pinvburr(q, shape1, shape2, rate = 1, scale = 1/rate,
         lower.tail = TRUE, log.p = FALSE)
qinvburr(p, shape1, shape2, rate = 1, scale = 1/rate,
         lower.tail = TRUE, log.p = FALSE)
rinvburr(n, shape1, shape2, rate = 1, scale = 1/rate)
minvburr(order, shape1, shape2, rate = 1, scale = 1/rate)
levinvburr(limit, shape1, shape2, rate = 1, scale = 1/rate,
           order = 1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. If length(n) > 1, the length is taken to be the number required.
shape1, shape2, scale parameters. Must be strictly positive.
rate an alternative way to specify the scale.
log, log.p logical; if TRUE, probabilities/densities p are returned as log(p).
lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
order order of the moment.
limit limit of the loss variable.

Details

The Inverse Burr distribution with parameters shape1 = a, shape2 = b and scale = s, has density:

f(x) = a b (x/s)^(ba)/(x [1 + (x/s)^b]^(a + 1))

for x > 0, a > 0, b > 0 and s > 0.

The Inverse Burr is the distribution of the random variable

s (X/(1 - X))^(1/b),

where X has a Beta distribution with parameters a and 1.

The Inverse Burr distribution has the following special cases:

The kth raw moment of the random variable X is E[X^k] and the kth limited moment at some limit d is E[min(X, d)^k].

Value

dinvburr gives the density, invburr gives the distribution function, qinvburr gives the quantile function, rinvburr generates random deviates, minvburr gives the kth raw moment, and levinvburr gives the kth moment of the limited loss variable.
Invalid arguments will result in return value NaN, with a warning.

Note

Also known as the Dagum distribution.

Author(s)

Vincent Goulet vincent.goulet@act.ulaval.ca and Mathieu Pigeon

References

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2004), Loss Models, From Data to Decisions, Second Edition, Wiley.

Examples

exp(dinvburr(2, 3, 4, 5, log = TRUE))
p <- (1:10)/10
pinvburr(qinvburr(p, 2, 3, 1), 2, 3, 1)
minvburr(2, 1, 2, 3) - minvburr(1, 1, 2, 3) ^ 2
levinvburr(10, 1, 2, 3, order = 2)
[Package actuar version 1.0-2 Index]