On Numerical Estimation of Joint Probability Distribution from Lebesgue Integral Quadratures
share
An important application of introduced in [1] Lebesgue integral quadrature is developed. Given two random processes f(x) and g(x) two generalized eigenvalues problems can be formulated and solved. Besides obtaining two Lebesgue quadrature (for f and g), projections of f-- and g-- eigenvectors on each other allow to build joint distribution estimator. Two kind of estimators are obtained: value--correlation V_f_i;g_j, that is similar to regular correlation concept, and a new one, probability--correlation P_f_i;g_j. The theory is implemented numerically, the software is available under GPLv3 license.
READ FULL TEXT