View source: R/covariance_matrix.R
U_ghuv | R Documentation |
It is used when random variables do not have finite second moments, and thus, the covariance matrix is not defined. For X= \int_{\R} g_s dL_s and Y= \int_{\R} h_s dL_s with \| g \|_{α}, \| h\|_{α}< ∞. Then the measure of dependence is given by U_{g,h}: \R^2 \to \R via
U_{g,h} (u,v)=\exp(- σ^{α}{\| ug +vh \|_{α}}^{α} ) - \exp(- σ^{α} ({\| ug \|_{α}}^{α} + {\| vh \|_{α}}^{α}))
U_ghuv(alpha, sigma, g, h, u, v, ...)
alpha |
self-similarity parameter of alpha stable random motion. |
sigma |
Scale parameter of lfsm |
g, h |
functions g,h: \R \to \R with finite alpha-norm (see |
v, u |
real numbers |
... |
additional parameters to pass to U_gh and U_g |
g<-function(x) exp(-x^2) h<-function(x) exp(-abs(x)) U_ghuv(alpha=1.5, sigma=1, g=g, h=h, u=10, v=15, rel.tol = .Machine$double.eps^0.25, abs.tol=1e-11)
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