GpdDistribution {fExtremes} | R Documentation |
A collection and description of functions to compute
the generalized Pareto distribution. The
functions compute density, distribution function,
quantile function and generate random deviates
for the GPD. In addition functions to
compute the true moments and to display the distribution
and random variates changing parameters interactively
are available.
The GPD distribution functions are:
dgpd | Density of the GPD Distribution, |
pgpd | Probability function of the GPD Distribution, |
qgpd | Quantile function of the GPD Distribution, |
rgpd | random variates from the GEV distribution, |
gpdMoments | computes true mean and variance, |
gpdSlider | displays density or rvs from a GPD. |
dgpd(x, xi = 1, mu = 0, beta = 1, log = FALSE) pgpd(q, xi = 1, mu = 0, beta = 1, lower.tail = TRUE) qgpd(p, xi = 1, mu = 0, beta = 1, lower.tail = TRUE) rgpd(n, xi = 1, mu = 0, beta = 1) gpdMoments(xi = 1, mu = 0, beta = 1) gpdSlider(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 |
[gpdSlider] - a character string denoting what should be displayed. Either the density and "dist" or random variates "rvs" .
|
n |
[rgpd][gpdSim - the number of observations to be generated. |
p |
a vector of probability levels, the desired probability for the quantile estimate (e.g. 0.99 for the 99th percentile). |
q |
[pgpd] - a numeric vector of quantiles. |
x |
[dgpd] - a numeric vector of quantiles. |
xi, mu, beta |
xi is the shape parameter,
mu the location parameter,
and beta is the scale parameter.
|
All values are numeric vectors:
d*
returns the density,
p*
returns the probability,
q*
returns the quantiles, and
r*
generates random deviates.
Alec Stephenson for the functions from R's evd
package,
Alec Stephenson for the functions from R's evir
package,
Alexander McNeil for the EVIS functions underlying the evir
package,
Diethelm Wuertz for this R-port.
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.
## rgpd - par(mfrow = c(2, 2), cex = 0.7) r = rgpd(n = 1000, xi = 1/4) seriesPlot(r) ## dgpd - # Plot empirical density and compare with true density: # Omit values greater than 500 from plot hist(r, n = 50, probability = TRUE, xlab = "r", col = "steelblue", border = "white", xlim = c(-1, 5), ylim = c(0, 1.1), main = "Density") box() x = seq(-5, 5, by = 0.01) lines(x, dgpd(x, xi = 1/4), col = "orange") ## pgpd - # Plot df and compare with true df: plot(sort(r), (1:length(r)/length(r)), xlim = c(-3, 6), ylim = c(0, 1.1), pch = 19, cex = 0.5, ylab = "p", xlab = "q", main = "Probability") grid() q = seq(-5, 5, by = 0.1) lines(q, pgpd(q, xi = 1/4), col = "steelblue") ## qgpd - # Compute quantiles, a test: qgpd(pgpd(seq(-1, 5, 0.25), xi = 1/4 ), xi = 1/4)