The coefficient of L-variation is computed by Lcomoment.coefficients(L1,L2)
where L1
is a 1st-order L-moment matrix and L2
is a \(k = 2\) L-comoment matrix. Symbolically, the coefficient of L-covariation is
$$ \hat{\tau}_{[12]} = \frac{\hat{\lambda}_{2[12]}}
{\hat{\lambda}_{1[12]}} \mbox{.}$$
The higher L-comoment coefficients (L-coskew, L-cokurtosis, ...) are computed by the function Lcomoment.coefficients(L3,L2)
(\(k=3\)), Lcomoment.coefficients(L4,L2)
(\(k=4\)), and so on. Symbolically, the higher L-comoment coefficients for \(k \ge 3\) are
$$ \hat{\tau}_{k[12]} = \frac{\hat{\lambda}_{k[12]}}
{\hat{\lambda}_{2[12]}}\mbox{.}$$
Finally, the usual univariate L-moment ratios as seen from lmom.ub
or lmoms
are along the diagonal. The Lcomoment.coefficients
function does not make use of lmom.ub
or lmoms
.