Density estimation of simulation output using exponential epi-splines

The density of stochastic simulation output provides more information on system performance than the mean alone. However, density estimation methods may require large sample sizes to achieve a certain accuracy or desired structural properties. A nonparametric estimation method based on exponential epi-splines has shown promise to overcome this difficulty by incorporating qualitative and quantitative information that reduces the space of possible density estimates substantially. Such `soft´ information may come in the form of the knowledge of a non-negative support, unimodality, and monotonicity, and is often available in simulation applications. We examine this method for output analysis of stochastic systems with fixed input parameters, and for a model with stochastic input parameters, with an emphasis on the use of derivative information.