GevDistribution {fExtremes} | R Documentation |
A collection and description of functions to compute
the generalized extreme value distribution. The
functions compute density, distribution function,
quantile function and generate random deviates
for the GEV including the Frechet, Gumbel, and
Weibull distributions. In addition functions to
compute the true moments and to display the distribution
and random variates changing parameters interactively
are available.
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. |
dgev(x, xi = 1, mu = 0, beta = 1, log = FALSE) pgev(q, xi = 1, mu = 0, beta = 1, lower.tail = TRUE) qgev(p, xi = 1, mu = 0, beta = 1, lower.tail = TRUE) rgev(n, xi = 1, mu = 0, beta = 1) gevMoments(xi = 0, mu = 0, beta = 1) gevSlider(method = c("dist", "rvs"))
log |
a logical, if TRUE , the log density is returned.
|
lower.tail |
a logical, if TRUE , the default, then
probabilities are P[X <= x] , otherwise, P[X > x] .
|
method |
[gevSlider] - a character sgtring denoting what should be displayed. Either the density and "dist" or random variates "rvs" .
|
n |
[rgev] - the number of observations. |
p |
[qgev] - a numeric vector of probabilities. [hillPlot] - probability required when option quantile is
chosen.
|
q |
[pgev] - a numeric vector of quantiles. |
x |
[dgev] - a numeric vector of quantiles. |
xi, mu, beta |
[*gev] - xi is the shape parameter, mu the location parameter,
and beta is the scale parameter. The default values are
xi=1 , mu=0 , and beta=1 . Note, if xi=0
the distribution is of type Gumbel.
|
d*
returns the density,
p*
returns the probability,
q*
returns the quantiles, and
r*
generates random variates.
All values are numeric vectors.
Alec Stephenson for R's evd
and evir
package, and
Diethelm Wuertz for this R-port.
Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.
## 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)