Abstract
Utilization of joint stochastic nature of timber strength properties such as elasticity and bending strength often produces good results. For example, the mechanical grading method provided an advanced system of allowable stresses. Statistical and visual expression methods are necessary for analyzing bivariate non-normal distributed data such as bivariate strength properties of timber. A probability ellipse is a graphical method for representing a bivariate distribution with specified inner probability. However it is not suitable for non-normal distributions. This report presents a method for drawing a skewed probability ellipse with marginal non-normal distributions. This method converts a conventional probability ellipse into a quantile-based non-normal ellipse using iso-probabilistic transformations based on marginal distributions. We have verified the following performances of the method by numerical experiments using some groups of accumulated data of tests in bending. The performances included accuracy of inner probability, uniformity of probability for de-correlated vectorial angle, and comparability among some data groups. These results confirmed that the method showed good performances.
