mistr (version 0.0.6)

Burr: The Burr Distribution

Description

Density, distribution function, quantile function and random generation for the Burr distribution with parameters shape1 and shape2.

Usage

dburr(x, shape1, shape2, log = FALSE)
pburr(q, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
qburr(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
rburr(n, shape1, shape2)

Value

dburr gives the density, pburr gives the distribution function, qburr gives the quantile function, and rburr generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

Arguments

x, q

vector of quantiles.

shape1

shape parameter.

shape2

shape parameter.

log, log.p

logical; if TRUE, probabilities \(p\) are given as \(log(p)\), default: FALSE.

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\), default: TRUE.

p

vector of probabilities.

n

number of observations.

Details

The Burr distribution function with shape1 parameter c and shape2 parameter k has density given by $$f(x)=ckx^(c-1)/(1+x^c)^(k+1)$$ for \(x>0\). The cumulative distribution function is $$F(x)=1-(1+x^c)^-k$$ on \(x>0\).

See https://en.wikipedia.org/wiki/Burr_distribution for more details.

See Also

burrdist

Examples

dburr(seq(1, 5), 2, 2)
qburr(pburr(seq(1, 5), 2, 2), 2 ,2)
rburr(5, 2, 2)