When an experiment is conducted, such as tossing coins, rolling a die, sampling for estimating the proportion of defective units, several outcomes or events occur with certain probabilities. These events or outcomes may be regarded as a variable which takes different values and each value is associated with a probability. The values of this variable depends on chance or probability. Such a vari...

Abstrac: This article surveys several classes of iterative methods for constructing random probability distributions (or random convex functions, or random home­ omorphisms), and includes illustrative applications in statistics, optimal-control theory, and game theory. Computer simulations of these methods are fast and easy to implement.

Learning Probability Distributions

An incremental, nonparametric probability estimation procedure using the fuzzy ARTMAP (adaptive resonance theory-supervised predictive mapping) neural network is introduced. In the slow-learning mode, fuzzy ARTMAP searches for patterns of data on which to build ever more accurate estimates. In max-nodes mode, the network initially learns a fixed number of categories, and weights are then adjust...