Decision Trees with Continuous Distribution

Abstract

Decision trees are often used as a convenient way to visualize, and then solve, a decision problem. A standard problem approached in this way is a decision as to whether or not to sample, followed by a decision whether or not to engage in an activity. This approach has been limited to a small number of sample outcomes to be practical. This paper develops an approach which permits a continuous distribution of sample outcomes to be used. A new distribution, the "skewed parabolic distribution" is introduced as a flexible way of representing the judgemental (probabilistic) beliefs of the assessor. This new distribution is compared with the beta distribution. An algorithm, which is easily programmed and is practical for hand computation with a calculator and logarithm tables, is developed for the complete solution of a decision tree problem using this skewed parabolic distribution. An example is given. It is concluded that the skewed parabolic distribution makes use of continuous distributions practical for decision trees, and has advantages over the beta for this purpose.