Analytic Jacobian of log-cumulants with respect to parameters

Returns the analytic Jacobian \(\mathbf{J}_{\mathcal{V}} = \partial \kappa_{\mathcal{V}} / \partial \theta\) for the selected set of cumulant orders, used in the construction of the \(T^2\) statistics.

Usage

jacobian_J(dist, theta, V)

Arguments

dist

Character; distribution name.

theta

Numeric length-2 parameter vector.

V

Integer vector of cumulant orders (e.g. c(2,3)).

Value

A length(V) by 2 numeric matrix.

Examples

jacobian_J("Weibull", c(2, 1), V = c(2, 3))
#>            [,1] [,2]
#> [1,] -0.4112335    0
#> [2,]  0.4507713    0