BurrXII: The Extended Burr type XII distribution
In hydroApps: Tools and models for hydrological applications

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

Density, distribution function and quantile function for the Extended (three-parameter) Burr type XII with scale parameter lambda and shape parameters k and c.

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	pBurrXII(x, lambda, k, c)
	dBurrXII(x, lambda, k, c)
	qBurrXII(p, lambda, k, c)

`x`	vector of quantiles.
`p`	vector of probabilities.
`lambda, k, c`	respectively the scale parameter and the two shape parameters.

The cumulative function of the extended Burr XII distribution reads:

P(x) = 1-≤ft(1-k ≤ft(\frac{x}{λ}\right)^c\right)^{1/k} \quad k \neq 0

P(x) = 1 - \exp ≤ft[ -≤ft(\frac{x}{λ}\right)^c\right] \quad k = 0

where x is the quantile, P is the non-exceedance probability, λ is the scale parameter and k and c are the shape parameters.

The range of the distribution is 0 ≤ x ≤ ∞ for k ≤ 0 and 0 ≤ x ≤ λ k^{-1/c} otherwise.

dBurrXII gives the density, pBurrXII gives the distribution function and qBurrXII gives the quantile function. The length of the result is determined by the length of x or p vectors.

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

lmomBurrXII, parBurrXII.approx

hydroApps documentation built on May 1, 2019, 10:30 p.m.