A method to replace a continuous univariate distribution with a discrete distribution that takes MN different values is analysed. Both distributions share the same rth moments for r = 0,..., 2N - 1 ...

where \(\mathsf{G}(\cdot)\) is some convex operator and \(\mathcal{F}\) is as set of feasible input distributions. Examples of such an optimization problem include finding capacity in information ...

The well-developed theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the ...