See http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution for an introduction to the GEV distribution.Definition
Parameters (3): $\xi$ (location), $\alpha$ (scale), $k$ (shape).
Range of $x$: $-\infty < x \le \xi + \alpha / k$ if $k>0$;
$-\infty < x < \infty$ if $k=0$;
$\xi + \alpha / k \le x < \infty$ if $k<0$.< p="">
Probability density function:
$$f(x) = \alpha^{-1} e^{-(1-k)y - e^{-y}}$$
where $y = -k^{-1}\log{1 - k(x - \xi)/\alpha}$ if $k \ne 0$,
$y = (x-\xi)/\alpha$ if $k=0$.
Cumulative distribution function:
$$F(x) = e^{-e^{-y}}$$
Quantile function:
$x(F) = \xi + \alpha[1-(-\log F)^k]/k$ if $k \ne 0$,
$x(F) = \xi - \alpha \log(-\log F)$ if $k=0$.
$k=0$ is the Gumbel distribution; $k=1$ is the reverse exponential distribution.
L-moments
L-moments are defined for $k>-1$.
$$\lambda_1 = \xi + \alpha[1 - \Gamma (1+k)]/k$$
$$\lambda_2 = \alpha (1-2^{-k}) \Gamma (1+k)]/k$$
$$\tau_3 = 2(1-3^{-k})/(1-2^{-k})-3$$
$$\tau_4 = [5(1-4^{-k})-10(1-3^{-k})+6(1-2^{-k})]/(1-2^{-k})$$
Here $\Gamma$ denote the gamma function
$$\Gamma (x) = \int_0^{\infty} t^{x-1} e^{-t} dt$$
Parameters
To estimate $k$, no explicit solution is possible, but the following approximation has accurancy better than $9 \times 10^{-4}$ for $-0.5 \le \tau_3 \le 0.5$:
$$k \approx 7.8590 c + 2.9554 c^2$$
where
$$c = \frac{2}{3+\tau_3} - \frac{\log 2}{\log 3}$$
The other parameters are then given by
$$\alpha = \frac{\lambda_2 k}{(1-2^{-k})\Gamma(1+k)}$$
$$\xi = \lambda_1 - \alpha[1 - \Gamma(1+k)]/k$$
Lmom.GEV and par.GEV accept input as vectors of equal length. In f.GEV, F.GEV, invF.GEV and rand.GEV parameters (xi, alfa, k) must be atomic.