homtest (version 0.1-4)

KAPPA: Four parameter kappa distribution

Description

KAPPA provides the link between L-moments of a sample and the four parameter kappa distribution.

Usage

f.kappa (x,xi,alfa,k,h)
F.kappa (x,xi,alfa,k,h)
invF.kappa (F,xi,alfa,k,h)
Lmom.kappa (xi,alfa,k,h)
par.kappa (lambda1,lambda2,tau3,tau4)
rand.kappa (numerosita,xi,alfa,k,h)

Arguments

x

vector of quantiles

xi

vector of kappa location parameters

alfa

vector of kappa scale parameters

k

vector of kappa third parameters

h

vector of kappa fourth parameters

F

vector of probabilities

lambda1

vector of sample means

lambda2

vector of L-variances

tau3

vector of L-CA (or L-skewness)

tau4

vector of L-kurtosis

numerosita

numeric value indicating the length of the vector to be generated

Value

• 'f.kappa' gives the density (f), 'F.kappa' gives the distribution function (F), 'invFkappa' gives the quantile function (x), 'Lmom.kappa' gives the L-moments (lambda1, lambda2, tau3, tau4), 'par.kappa' gives the parameters (xi, alfa, k, h), and 'rand.kappa' generates random deviates.

Details

'Lmom.kappa' and 'par.kappa' accept input as vectors of equal length. In 'f.kappa', 'F.kappa', 'invF.kappa' and 'rand.kappa' parameters (xi,alfa,k,h) must be atomic.

References

Hosking, J.R.M. and Wallis, J.R. (1997) Regional Frequency Analysis: an approach based on L-moments, Cambridge University Press, Cambridge, UK.

See Also

HOMTESTS, rnorm, runif

Examples

data(annualflows)
annualflows
summary(annualflows)
x <- annualflows["dato"][,]
fac <- factor(annualflows["cod"][,])
split(x,fac)

camp <- split(x,fac)$"45"
ll <- Lmoments(camp)
parameters <- par.kappa(ll[1],ll[2],ll[4],ll[5])
f.kappa(1800,parameters$xi,parameters$alfa,parameters$k,parameters$h)
F.kappa(1800,parameters$xi,parameters$alfa,parameters$k,parameters$h)
invF.kappa(0.771088,parameters$xi,parameters$alfa,parameters$k,parameters$h)
Lmom.kappa(parameters$xi,parameters$alfa,parameters$k,parameters$h)
rand.kappa(100,parameters$xi,parameters$alfa,parameters$k,parameters$h)

Rll <- regionalLmoments(x,fac); Rll
parameters <- par.kappa(Rll[1],Rll[2],Rll[4],Rll[5])
Lmom.kappa(parameters$xi,parameters$alfa,parameters$k,parameters$h)