fExtremes (version 251.70)

GevDistribution: Generalized Extreme Value Distribution

Description

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: ll{ 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]<="" code="">, 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 x

Value

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

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)