Continuous Density Approximation on a Bounded Interval Using Information Theoretic Concepts.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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This report presents the theoretical development and numerical implementation of a procedure for approximating continuous probability density functions on a bounded interval. The work is applicable to Bayesian decision models and that available information is used to update or obtain the prior distribution. The procedure is based on the solution of a constrained entropy maximization problem and requires information in the form of expected values of information functions. The approach involves three steps estimation of expected or average values of potential information functions, selection of the active subset of functions to define the approximation family, and simultaneous solution of the constraints to select the specific approximating density for a given set of data. A useful set of potential information functions is developed, and three numerical methods for active set selection are demonstrated. Numerical techniques for expected value computation are discussed, and a scheme for solution of the constraints is developed and implemented. Theoretical development includes theorems on form and uniqueness. Approximation accuracy is related to potential set definition and data accuracy. The procedure is applied to several known distributions to demonstrate applicability. Applications to computer simulation and interval arithmetic models are demonstrated with specific examples. Author
- Statistics and Probability