The kappa version of a generating function \(\psi\) is defined as \(\kappa(x) = \psi(x) + x \psi'(x)\). igl_kappa takes \(\psi\) to be the IGL generating function, igl_gen().

y_igl_kappa(x, alpha)

y_igl_kappa_D(x, alpha)

y_igl_kappa_inv(p, alpha)

Arguments

x

Numeric argument of the kappa function. Vectorized.

alpha

Parameter of the IGL generating function, igl_gen(), >0. Vectorized.

p

Numeric argument of the inverse function. Vectorized. Between 0 and 1, inclusive.

Details

igl_kappa_D() is the derivative; igl_kappa_inv() is the inverse.