KAPPA: Kappa Distribution

In FAdist: Distributions that are Sometimes Used in Hydrology

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].

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)

Value

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

Examples

x <- rkappa(1000,12,10)
hist(x,freq=FALSE,col='gray',border='white')
curve(dkappa(x,12,10),add=TRUE,col='red4',lwd=2)

FAdist documentation built on March 18, 2022, 5:24 p.m.