Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions

摘要: The paper provides a condition for differentiability as well an equivalent criterion Lipschitz continuity of singular normal distributions. Such distributions are interest, instance, in stochastic optimization problems with probabilistic constraints, where comparatively small (nondegenerate-) normally distributed random vector induces large number linear inequality constraints (e.g. networks demands). is established the class quasi-concave which distribution belongs to.