Non-Normal Probability Ellipse for Representing Bivariate Data of the Strength Properties of Timber II.

Abstract

This report presents a method for drawing a non-normal probability ellipse with constant probability density (dNNE). In other words, dNNE is a probability density contour for which inner probability is specified. The aim of this study is to develop modeling and visualization techniques for bivariate nonnormal distributed data such as elasticity and strength of timber. We have mathematically examined probability density contours of bivariate distributions and inner probabilities of the contours, and a numerical calculation method for drawing dNNE was obtained. A procedure for evaluating the probability of a data region enclosed by a closed curve was introduced into this method. We have verified the following performances of the method by numerical experiments using some groups of accumulated timber strength data in bending. The performances included suitability of probability density contours, accuracy of inner probabilities, and visual expressiveness for bivariate data. These results confirmed that the method showed good performances.