Gumbel (extreme-value type I) distribution
Distribution function and quantile function of the Gumbel distribution.
cdfgum(x, para = c(0, 1)) quagum(f, para = c(0, 1))
x |
Vector of quantiles. |
f |
Vector of probabilities. |
para |
Numeric vector containing the parameters of the distribution, in the order xi, alpha (location, scale). |
The Gumbel distribution with location parameter xi and scale parameter alpha has distribution function
F(x) = exp(-exp(-(x-xi)/alpha))
and quantile function
x(F) = xi - alpha log(-log F) .
cdfgum gives the distribution function;
quagum gives the quantile function.
The functions expect the distribution parameters in a vector,
rather than as separate arguments as in the standard R
distribution functions pnorm, qnorm, etc.
cdfgev for the generalized extreme-value distribution,
which generalizes the Gumbel distribution.
# Random sample from the Gumbel distribution with parameters xi=0, alpha=3. quagum(runif(100), c(0,3))
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