Q: Can you explain how the values and probabilities of a node's branches are generated when I choose to base them on a probability distribution in the Branch Definition dialog?
A: The section of the PrecisionTree User's Guide detailing the algorithm used for generating values and probabilities based on a distribution (distributed chance nodes) is somewhat vague. A more detailed description of these algorithms is given below.
Fixed Value: The fixed value option creates equally spaced "bins" across the maximum and minimum range of the distribution you specify. The number of bins is the number of branches originating from the chance node. It then calculates the probabilities associated with the midpoints of these bins, and normalizes them to unity. The midpoint "x" values become the chance node's payoff values, while the normalized probabilities become the branch probabilities. If a distribution is asymptotic (in other words there is no finite minimum or maximum value) then the minimum value is where the cumulative distribution function reaches 1% and the maximum value is where the cumulative distribution reaches 99%.
Fixed Probability: The fixed probability option divides 100% by the number of branches to get the probability for each branch. To determine the corresponding values, the cumulative distribution function is divided into equally sized "bins" of probability. The value associated with each branch is the corresponding x-value of the midpoints of each of these bins.
