FAdist (version 2.4)

KAPPA: Kappa Distribution

Description

Density, distribution function, quantile function and random generation for the kappa distribution with shape and scale parameters equal to shape and scale, respectively.

Usage

dkappa(x,shape=1,scale=1,log=FALSE)
pkappa(q,shape=1,scale=1,lower.tail=TRUE,log.p=FALSE)
qkappa(p,shape=1,scale=1,lower.tail=TRUE,log.p=FALSE)
rkappa(n,shape=1,scale=1)

Arguments

x,q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

shape

shape parameter.

scale

scale parameter.

log,log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Value

dkappa gives the density, pkappa gives the distribution function, qkappa gives the quantile function, and rkappa generates random deviates.

Details

If X is a random variable distributed according to a kappa distribution, it has density

f(x) = shape/scale*(shape+(x/scale)^shape)^(-(shape+1)/shape)

Examples

# NOT RUN {
x <- rkappa(1000,12,10)
hist(x,freq=FALSE,col='gray',border='white')
curve(dkappa(x,12,10),add=TRUE,col='red4',lwd=2)
# }