Gumbel {QRMlib}R Documentation

Gumbel Distribution

Description

Density, quantiles, and cumulative probability of the Gumbel distribution. The standard Gumbel has mu value of 0 and sigma value of 1.

Usage

dGumbel(x, mu=0, sigma=1, logvalue=FALSE) 
qGumbel(p, mu=0, sigma=1) 
pGumbel(q, mu=0, sigma=1)
rGumbel(n, mu=0, sigma=1)

Arguments

x vector of values at which to evaluate density or cdf
q vector of quantiles
p vector of probabilities
mu location parameter of Gumbel distribution
sigma scale parameter (sigma >= 0) of Gumbel distribution
logvalue whether or not log values of density should be returned (useful for ML)
n number of values to simulate for random Gumbel

Value

Probability (pGumbel), quantile (qGumbel), density (dGumbel) and random vector (rGumbel) for the Gumbel distribution with location parameter mu and scale parameter sigma.

Examples

#Simulate 1000 Gumbel variates:
rGumbelSim <- rGumbel(1000, 1.0, 2.5);
#Compare cdf of GEV to that of Gumbel when xi = 0 with location parameter 1 and scale 2.5
quantValue <- 4.5;
pG <- pGEV(q=quantValue, xi=0, mu=1.0, sigma=2.5) 
pg <- pGumbel(q=quantValue, mu=1.0, sigma=2.5);

[Package QRMlib version 1.4.4 Index]