For many decades, the problem of estimating a pdf based on measurements has been of interest to many researchers. Even though much work has been done in the area of pdf estimation, most of it was focused on the continuous case. In this paper, we propose a new model based approach for estimating a discrete probability density function. This approach is based on multirate dsp theory, and it has s...

The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function valu...

It is known that probability density functions and probability mass functions can usually be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions, respectively) with the Fourier-series method, but other more general functions can be substantially more difficult to invert, because the aliasing and roundoff errors tend to be more difficult...