Analysis of the characteristic features of the density functions for gamma, Weibull and log-normal distributions through RBF network pruning with QLP

The Weibull, Gamma and Log-normal densities are similar in shape for the same coefficient of variation, making it difficult to identify the differences between the three densities. This paper is concerned with separating these three probability densities using feature descriptors, identified by pruning a Radial Basis Function (RBF) network using pivoted QLP decomposition generated for each density function with the same mean and coefficients of variation. The QLP method proves efficient for reducing the network size by pruning hidden nodes, resulting is a parsimonious model which identifies four main features (namely kurtosis, skewness, inter-quartile range and mean). This application tool can be used to identify the correct distribution function from empirical data in cases where traditional statistical tests are inconclusive. Key-Words: Radial Basis Function, Pivoted QLP Decomposition, probability density function.