Bivariate logistic max-stable distribution

Formula: F(x,y) = exp(-((x^(-1/alpha) + y^(-1/alpha))^alpha))

Usage

Evmsexp(x, y, alpha)

Arguments

x: First coordinate, strictly positive (unit Frechet scale).
y: Second coordinate, strictly positive.
alpha: Dependence parameter in (0, 1].

Value

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

Details

Coles (2001) eq. (8.10), p. 146, on unit Frechet margins. As alpha -> 1 the exponent becomes 1/x + 1/y and the margins are independent; as alpha -> 0 it becomes max(1/x, 1/y) and they are perfectly dependent. The Pickands function of this family is A(t) = (t^(1/alpha) + (1-t)^(1/alpha))^alpha and the coefficient of upper tail dependence is 2 - 2^alpha.

References

Tawn (1988), Biometrika 75(3):397-415; Coles (2001), An Introduction to Statistical Modeling of Extreme Values, Springer, eq. (8.10) p. 146.

Examples

Evmsexp(x = c(1, 2, 3, 4, 5, 6, 7, 8), y = c(1, 2, 3, 4, 5, 6, 7, 8), alpha = 0.5)
#> $F
#> [1] 0.2431167 0.4930687 0.6241251 0.7021885 0.7536383 0.7900159 0.8170700
#> [8] 0.8379669
#> 
#> $estimate
#> [1] 0.2431167
#> 
#> $V
#> [1] 1.4142136 0.7071068 0.4714045 0.3535534 0.2828427 0.2357023 0.2020305
#> [8] 0.1767767
#> 
#> $A_half
#> [1] 0.7071068
#> 
#> $chi
#> [1] 0.5857864
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "bivariate logistic max-stable distribution"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"