BurrXII_param: Parameters of the Extended Burr type XII distribution
In hydroApps: Tools and models for hydrological applications

Description Usage Arguments Details Value Author(s) References See Also Examples

Compute the parameters of the Extended Burr XII given the L-moments with some approximated functions.

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	parBurrXII.approx(L1, tau, tau3)
	tau3BurrXII.WeibullBound(tau)
	tau3BurrXII.ParetoBound(tau)

`L1`	the mean of the distribution.
`tau`	the L-CV of the distribution.
`tau3`	the L-skewness of the distribution.

parBurrXII.approx computes the shape parameters using the approximated equations in Ganora and Laio (2014). Note that the approximated equations are valid only for k ≤ 0 (distribution without upper bound). Please refer to Ganora and Laio (2014) for details about the equations.

tau3BurrXII.WeibullBound and tau3BurrXII.ParetoBound are mostly used as internal functions, but can be useful for static plots and data interpretation. They represents the upper and lower bound of the distribution domain over the τ-tau_3 space.

parBurrXII.approx provides a vector of three elements which are the parameters of the distribution. tau3BurrXII.WeibullBound provide the minimum value of τ_3 compatible with tau (corresponding to the lower bound in the τ-τ_3 space, i.e. when k=0). tau3BurrXII.paretoBound provide the maximum value of tau_3 compatible with tau (corresponding to the upper bound in the τ-τ_3 space, i.e. when k tends to ∞)

Daniele Ganora

D. Ganora and F. Laio. Hydrological applications of the Burr distribution: a practical method for parameter estimation. Submitted to Journal of Hydrologic Engineering (ASCE).

Z. Hao and V.P. Singh. Entropy-based parameter estimation for extended Burr XII distribution. Stoch. Environ. Res. Risk. Assess. (2009) 23:1113-1122

pBurrXII, dBurrXII, qBurrXII, lmomBurrXII

## compute parameters from L-moments
parburr <- parBurrXII.approx(L1=2, tau=0.45, tau3=0.51)
parburr 

## Not run: 
## plot the validity domain in the tau-tau3 space
tau = seq(0, 1, by=0.02)
plot(tau, tau3BurrXII.WeibullBound(tau), type="l", lwd=2, ylim=c(-.2, 1))
lines(tau, tau3BurrXII.ParetoBound(tau), lwd=2)

## End(Not run)