mistr (version 0.0.2)

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)

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.

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.

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

# NOT RUN {
dburr(seq(1, 5), 2, 2)
qburr(pburr(seq(1, 5), 2, 2), 2 ,2)
rburr(5, 2, 2)
# }