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Husler-Reiss bivariate dependence

Source: R/evhrid.R
Evhrid.Rd

Formula: F(x,y) = exp(-x Phi(lam + log(y/x)/(2 lam)) - y Phi(lam + log(x/y)/(2 lam)))

Usage

Evhrid(x, y, lam)

Arguments

x

First coordinate, strictly positive.

y

Second coordinate, strictly positive.

lam

Dependence parameter, strictly positive.

Value

List with F, estimate, V, A_half, chi, n, method.

Details

Written on the standard exponential scale, where each margin is exp(-x). As lam -> 0 the exponent tends to min(x, y), perfect dependence; as lam -> infinity it tends to x + y, independence.

References

Husler & Reiss (1989), Statist. Probab. Letters 7(4):283-286.

Examples

Evhrid(x = c(1, 2, 3, 4, 5, 6, 7, 8), y = c(1, 2, 3, 4, 5, 6, 7, 8), lam = 5L)
#> $F
#> [1] 1.353354e-01 1.831566e-02 2.478756e-03 3.354634e-04 4.540006e-05
#> [6] 6.144233e-06 8.315321e-07 1.125357e-07
#> 
#> $estimate
#> [1] 0.1353354
#> 
#> $V
#> [1]  1.999999  3.999999  5.999998  7.999998  9.999997 11.999997 13.999996
#> [8] 15.999995
#> 
#> $A_half
#> [1] 0.9999997
#> 
#> $chi
#> [1] 5.733031e-07
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Husler-Reiss bivariate extreme-value dependence"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"