Estimation of complicated distributions using B-spline functions

The distributions of some of random variables are quite complicated and difficult to determine using ordinary statistical models. A method is presented in this paper which gives satisfactory estimation of the complicated distribution of a continuous random variable. There are two key steps in the method: one being that the probability density function (p.d.f.) of a random variable is approximated by a linear combination of B-splines and the other being that the best model is determined by entropy analysis. Extensive numerical experiments have made it clear that the proposed method is useful to determine the p.d.f. directly from a set of sample points without using any prior knowledge of the distribution form.