Empirical chi(u) = 2 - log P(F_X < u, F_Y < u) / log u, with the
probabilities replaced by observed proportions of the rank transforms.
As u tends to one chi(u) tends to the upper tail dependence
coefficient: chi = 0 for asymptotic independence, chi = 1 for perfect
tail dependence. The joint proportion is bounded away from 0 and 1 by
half an observation so the logarithm stays finite, and chi is clamped
to [0, 1] (property 1, Coles p. 164).
Arguments
- x, y
Equal-length numeric vectors, n >= 4.
- u
Threshold in (0, 1), default 0.95.
Value
List with estimate, u, n, method.
Details
R arm of the existing Python chiDep module.
References
Coles, S. (2001). An Introduction to Statistical Modeling
of Extreme Values. Springer, section 8.4, pp. 163-165.
Examples
ChiDep(c(1, 2, 3, 4, 5, 6), c(1, 2, 3, 4, 5, 6), 0.5)
#> $estimate
#> [1] 1
#>
#> $u
#> [1] 0.5
#>
#> $n
#> [1] 6
#>
#> $method
#> [1] "empirical chi(u) (Coles 2001 sec. 8.4)"
#>
