POT (version 1.1-11)

bvgpd: Parametric Bivariate GPD

Description

Density, distribution function and random generation for six different parametric bivariate GPD

Usage

rbvgpd(n, alpha, model = "log", asCoef, asCoef1, asCoef2, mar1 =
c(0,1,0), mar2 = mar1)
pbvgpd(q, alpha, model = "log", asCoef, asCoef1, asCoef2, mar1 =
c(0,1,0), mar2 = mar1, lower.tail = TRUE)

Value

Generate a random vector of length n.

Arguments

n

The number of observations to be simulated.

q

A matrix or vector with two columns at which the distribution is computed.

alpha

Dependence parameter for the logistic, asymmetric logistic, negative logistic, asymmetric negative logistic, mixed and asymmetric mixed models.

model

The specified model; a character string. Must be either "log" (the default), "alog", "nlog", "anlog", "mix" or "amix", for the logistic, asymmetric logistic, negative logistic, asymmetric negative logistic, mixed and asymmetric mixed models respectively.

asCoef,asCoef1,asCoef2

The asymmetric coefficients for the asymmetric logistic, asymmetric negative logistic and asymmetric mixed models.

mar1,mar2

Vectors of length 3 giving the marginal parameters.

lower.tail

Logical. If TRUE (the default), P[X \(\leq\) x] is computed, else P[X \(\geq\) x].

Author

Mathieu Ribatet (Alec Stephenson for the C codes)

Details

The logistic and asymmetric logistic models respectively are simulated using bivariate versions of Algorithms 1.1 and 1.2 in Stephenson(2003). All other models are simulated using a root finding algorithm to simulate from the conditional distributions.

References

Stephenson, A. G. (2003) Simulating multivariate extreme value distributions of logistic type. Extremes, 6(1), 49--60.

Examples

x <- rbvgpd(1000, alpha = 0.25, model = "log", mar1 = c(0,1,0.25), mar2
= c(2,0.5, -0.15))
y <- rbvgpd(1000, alpha = 0.75, model = "nlog", mar1 = c(0,1,0.25), mar2
= c(2,0.5, -0.15))
par(mfrow=c(1,2))
plot(x);plot(y)