Statistical Measures, Probability Densities, and Mathematical Models for Stochastic Measurements

Statistical measures, probability densities, and mathematical modeling techniques useful in the analysis of stochastic measurements are summarized. Univariate measures are given for average, dispersion, skewness, and kurtosis. Probability Densities include: Normal, Student t, Cauchy, Gamma, Exponential, Chi-square, F, Rayleigh, Maxwell, Log-normal, Beta, Uniform, and Arc-sine. Measures of interdependence between two variables include simple correlation, autocorrelation, cross-correlation, rank correlation, point biserial correlation, tetrachoric correlation, and coefficients of contingency. Measures of interdependence among several variables include multiple correlation, marginal correlation, conditional correlation, canonical correlation, and auto and cross-correlation for ensembles of measurements. Mathematical modeling techniques include factor analysis and both regression and analysis of variance formulated as the general linear hypothesis model. (Author)