A visualization algorithm for the plane probability measure kernel

The authors propose an algorithm for constructing a probability measure kernel polyhedral approximation for a two-dimensional random vector with independent components. The kernel is one of the important concepts used in algorithms for solving stochastic programming problems with probabilistic criteria. The kernel is most effectively used in cases when the statements of the indicated problems have the property of linearity with respect to random parameters. Because of linearity, the maximum in random parameters is determined by searching all vertices of the approximating polyhedron. The authors propose an algorithm for constructing a polyhedral approximation of the kernel of a probability measure for a two-dimensional random vector with independent components. The algorithm is based on construction of the intersection of a finite number of confidence half-spaces, the parameters of which are estimated by the Monte-Carlo method. The result of the proposed algorithm is the definition of the set of vertices of the approximating polyhedron. Approximation of the nucleus is their convex hull. The results of calculations for a number of typical continuous distribution laws are presented.