Analysis of the probability distribution of small random samples by nonlinear fitting of integrated probabilities

Small random samples of biochemical and biological data are often representative of complex distribution functions and are difficult to analyze in detail by conventional means. The common approaches reduce the data to a few representative parameters (such as their moments) or combine the data into a histogram plot. Both approaches reduce the information content of the data. By fitting the empirical cumulative distribution function itself with models of integrated probability distributions, the information content of the raw data can be fully utilized. This approach, distribution analysis by nonlinear fitting of integrated probabilities, allows analysis of normally distributed samples, truncated data sets, and multimodal distributions with a single, powerful data processing procedure.