Statistical Procedures for Finding Distribution Fits over Datasets with Applications in Biochemistry

A common problem in statistics is finding a distribution that fits to a certain dataset. Many theoretical distributions have been developed to give a good description of the empirical observations, and consequently, theory offers a variety of algorithms to test the quality of the resulting fits. It is reasonable to expect that each set of measurements should be described with the same theoretical distribution if one and the same experimental mechanism was applied. This paper presents procedures to find a theoretical distribution that best fits to several datasets. The procedure goes further, answering the questions of whether the given datasets come from the same general population, and assessing if the difference between the fitted distributions of two datasets are statistically significant. Kuiper test is used in all steps of the analysis. In two of those a Monte Carlo simulation procedure is elaborated to construct the Kuiper statistic's distribution. A platform with original program functions in MATLAB R2009a is created on the basis of the described procedures. It is applied to datasets from a biochemical experiment, which investigates the resulting density of fibrin network under different thrombin concentrations. The developed procedure has wide applications in different fields, as it models the behavior of datasets, generated through the same mechanism. The possibility to fit one type of distribution over different datasets allows comparing samples, performing interpolation and extrapolation procedures, and investigating the influence of the input conditions of an experiment over the parameters of the fitted distributions.