# GevDistribution: Generalized Extreme Value Distribution In fExtremes: Rmetrics - Modelling Extreme Events in Finance

## 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``` ```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")) ```

## Arguments

 `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` a character sgtring denoting what should be displayed. Either the density and `"dist"` or random variates `"rvs"`. `n` the number of observations. `p` a numeric vector of probabilities. [hillPlot] - probability required when option `quantile` is chosen. `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. The default values are `xi=1`, `mu=0`, and `beta=1`. Note, if `xi=0` the distribution is of type Gumbel.

## 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 R-port.

## 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") ```

fExtremes documentation built on Nov. 17, 2017, 2:21 p.m.