New methods are presented for estimating univariate and bivariate Bezier distributions. A likelihood ratio test is used to estimate the number of control points for a univariate Bezier distribution fitted to sample data. To estimate the control points of a bivariate Bezier distribution with fixed marginals based on either sample data or subjective information about the joint dependency structure, a linear-programming approach is formulated. These methods are implemented in the Windows-based software system called PRIME-PRobabilistic Input Modeling Environment. Several examples illustrate the application of these estimation procedures.