GpdDistribution {fExtremes} | R Documentation

## GPD Distributions for Extreme Value Theory

### Description

A collection and description of distribution functions used in extreme value theory. The functions compute density, distribution function, quantile function and generate random deviates for the Generalized Pareto Distribution GPD.

The 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 GPD Distribution.

### Usage

    dgpd(x, xi = 1, mu = 0, beta = 1)
    pgpd(q, xi = 1, mu = 0, beta = 1)
    qgpd(p, xi = 1, mu = 0, beta = 1)
    rgpd(n, xi = 1, mu = 0, beta = 1)

### Arguments

`n` | the number of observations.
`p` | a numeric vector of probabilities.
`q` | a numeric vector of quantiles.
`x` | a numeric vector of quantiles.
`xi, mu, beta` | `xi` is the shape parameter, `mu` the location parameter, and `beta` is the scale parameter.

### Details

Generalized Pareto Distribution:
Compute density, distribution function, quantile function and generates random variates for the Generalized Pareto Distribution.

### Value

All values are numeric vectors:
`d*` returns the density,
`p*` returns the probability,
`q*` returns the quantiles, and
`r*` generates random deviates.

### Author(s)

Alec Stephenson for the functions from R's `evd` package,
Diethelm Wuertz for this R-port.

### References

Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.

### Examples

    ## SOURCE("fExtremes.53A-GpdModelling")

    ## *gpd  -
       xmpExtremes("\nStart: Simulate GPD Distributed sample >")
       par(mfrow = c(2, 2))
       r = rgpd(n = 1000, xi = 1/4)
       plot(r, type = "l", main = "GPD Series")

    ## Plot empirical density and compare with true density:
    ## Omit values greater than 500 from plot
       xmpExtremes("\nNext: Plot Empirical and True Density >")
       hist(r, n = 50, probability = TRUE, xlab = "r",
         xlim = c(-5, 5), ylim = c(0, 1.1), main = "Density")
       x = seq(-5, 5, by = 0.01)
       lines(x, dgpd(x, xi = 1/4), col = "steelblue3")

    ## Plot df and compare with true df:
       xmpExtremes("\nNext: Plot Empirical and True Probability >")
       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")
       q = seq(-5, 5, by = 0.1)
       lines(q, pgpd(q, xi = 1/4), col = "steelblue3")

    ## Compute quantiles, a test:
       xmpExtremes("\nNext: Compute Quantiles >")
       qgpd(pgpd(seq(-1, 5, 0.25), xi = 1/4 ), xi = 1/4)

[Package fExtremes version 221.10065 Index]