fExtremes: GevDistribution – R documentation

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GevDistribution

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

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

## 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

Rmetrics - Modelling Extreme Events in Finance

v3042.82

GPL (>= 2)

Authors

Diethelm Wuertz [aut], Tobias Setz [cre], Yohan Chalabi [ctb]

Initial release

2017-11-12