Generalized Extreme Value Distribution
Description
Density, distribution function, quantile function, random
number generation, and true moments for the GEV including
the Frechet, Gumbel, and Weibull distributions.
The GEV distribution functions are:
dgev  density of the GEV distribution, 
pgev  probability function of the GEV distribution, 
qgev  quantile function of the GEV distribution, 
rgev  random variates from the GEV distribution, 
gevMoments  computes true mean and variance, 
gevSlider  displays density or rvs from a GEV. 
Usage
1 2 3 4 5 6 7 8 
Arguments
log 
a logical, if 
lower.tail 
a logical, if 
method 
a character sgtring denoting what should be displayed. Either
the density and 
n 
the number of observations. 
p 
a numeric vector of probabilities.
[hillPlot]  
q 
a numeric vector of quantiles. 
x 
a numeric vector of quantiles. 
xi, mu, beta 

Value
d*
returns the density,
p*
returns the probability,
q*
returns the quantiles, and
r*
generates random variates.
All values are numeric vectors.
Author(s)
Alec Stephenson for R's evd
and evir
package, and
Diethelm Wuertz for this Rport.
References
Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34  ## rgev 
# Create and plot 1000 Weibull distributed rdv:
r = rgev(n = 1000, xi = 1)
plot(r, type = "l", col = "steelblue", main = "Weibull Series")
grid()
## dgev 
# Plot empirical density and compare with true density:
hist(r[abs(r)<10], nclass = 25, freq = FALSE, xlab = "r",
xlim = c(5,5), ylim = c(0,1.1), main = "Density")
box()
x = seq(5, 5, by = 0.01)
lines(x, dgev(x, xi = 1), col = "steelblue")
## pgev 
# Plot df and compare with true df:
plot(sort(r), (1:length(r)/length(r)),
xlim = c(3, 6), ylim = c(0, 1.1),
cex = 0.5, ylab = "p", xlab = "q", main = "Probability")
grid()
q = seq(5, 5, by = 0.1)
lines(q, pgev(q, xi = 1), col = "steelblue")
## qgev 
# Compute quantiles, a test:
qgev(pgev(seq(5, 5, 0.25), xi = 1), xi = 1)
## gevMoments:
# Returns true mean and variance:
gevMoments(xi = 0, mu = 0, beta = 1)
## Slider:
# gevSlider(method = "dist")
# gevSlider(method = "rvs")

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