Density function, distribution function, quantile function, random generation,
raw moments and limited moments for the Burr distribution with
dburr(x, shape1, shape2, rate = 1, scale = 1/rate, log = FALSE) pburr(q, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) qburr(p, shape1, shape2, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE) rburr(n, shape1, shape2, rate = 1, scale = 1/rate) mburr(order, shape1, shape2, rate = 1, scale = 1/rate) levburr(limit, shape1, shape2, rate = 1, scale = 1/rate, order = 1)
vector of quantiles.
vector of probabilities.
number of observations. If
parameters. Must be strictly positive.
an alternative way to specify the scale.
order of the moment.
limit of the loss variable.
The Burr distribution with parameters
shape1 = a,
shape2 = b and
= s has density:
f(x) = (a b (x/s)^b)/(x [1 + (x/s)^b]^(a + 1))
for x > 0, a > 0, b > 0 and s > 0.
The Burr is the distribution of the random variable
s (X/(1 - X))^(1/b),
where X has a beta distribution with parameters 1 and a.
The Burr distribution has the following special cases:
A Loglogistic distribution when
A Paralogistic distribution when
shape2 == shape1;
A Pareto distribution when
The kth raw moment of the random variable X is E[X^k], -shape2 < k < shape1 * shape2.
The kth limited moment at some limit d is E[min(X, d)^k], k > -shape2 and shape1 - k/shape2 not a negative integer.
dburr gives the density,
pburr gives the distribution function,
qburr gives the quantile function,
rburr generates random deviates,
mburr gives the kth raw moment, and
levburr gives the kth moment of the limited loss
Invalid arguments will result in return value
NaN, with a warning.
levburr computes the limited expected value using
Distribution also known as the Burr Type XII or Singh-Maddala distribution. See also Kleiber and Kotz (2003) for alternative names and parametrizations.
"distributions" package vignette provides the
interrelations between the continuous size distributions in
actuar and the complete formulas underlying the above functions.
Vincent Goulet email@example.com and Mathieu Pigeon
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.
dpareto4 for an equivalent distribution with a location
exp(dburr(1, 2, 3, log = TRUE)) p <- (1:10)/10 pburr(qburr(p, 2, 3, 2), 2, 3, 2) ## variance mburr(2, 2, 3, 1) - mburr(1, 2, 3, 1) ^ 2 ## case with shape1 - order/shape2 > 0 levburr(10, 2, 3, 1, order = 2) ## case with shape1 - order/shape2 < 0 levburr(10, 1.5, 0.5, 1, order = 2)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.