A Non-Parametric Probability Density Estimator and Some Applications.
Abstract
In this thesis a new non-parametric probability density estimator is developed which has the following properties: (1) It yields a continuous, non-negative and piecewise linear estimate of a probability density function. (2) It converges to the true density function if the true density has no more than a finite number of discontinuities of a form where the value of the function at the discontinuity can be considered the average of the limiting values on either side of the discontinuity. (3) It requires no user supplied parameters. The estimator is shown to have significantly better error properties, for certain classes of distributions, than existing density estimators. The quality of the estimate is discussed, tabulated and graphically demonstrated. Applications, including parameterization, small sample analysis, and two sample tests are presented. These newly developed applications are shown to improve upon the generally accepted existing techniques. Guidelines for choosing a density estimation method along with an organized approach to method selection are discussed. Key words include: Statistical functions, Statistical tests, Nonparametric statistics, Probability density functions, Statistics.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1984
- Accession Number
- ADA151853
Entities
People
- R. P. Fuchs
Organizations
- Air Force Institute of Technology