Estimation of the shape of probability density functions using deterministic algorithms

This paper describes algorithmic methods which result in a reasonable discrete estimate of the shape of a probability density function (pdf). A finite number of samples known to have been selected from the governing density function are used to iteratively develop these successively better estimates. Two classes of deterministic algorithms are described. The first class is heuristically derived, and the second class results from maximizing the entropy of the estimate as an index of performance. Variations of the algorithms are compared and results presented as to rate of convergence, limit cycle stability, and ease of implementation. The techniques may be readily applied to the approximation of non-linear functions by zero order quantizers, and extended to the n dimensional case.