Bounded Densities and Their Derivatives: Extension to Other Domains

This paper describes how one can compute interval-valued statistical measures given limited information about the underlying distribution. The particular focus is on a bounded derivative of a probability density function and its combination with other available statistical evidence for computing quantities of interest. To be able to utilise the evidence about the derivative it is suggested to adapt the ‘conventional’ problem statement to variational calculus and the way to do so is demonstrated. A number of examples are given throughout the paper.