Random Sampling Using $k$k-Vector

This paper introduces two new techniques for random number generation with any prescribed nonlinear distribution based on the
$k$
-vector methodology. The first approach is based on an inverse transform sampling using the optimal
$k$
-vector to generate the samples by inverting the cumulative distribution. The second approach generates samples by performing random searches in a pregenerated large database previously built by massive inversion of the prescribed nonlinear distribution using the
$k$
-vector. Both methods are shown to be suitable for massive generation of random samples. Examples are provided to clarify these methodologies.