Abstract
In real world statistical applications a large class of univariate probability distributions are unimodal. This paper presents a neural network approach to probability density estimation for univariate unimodal data. This approach is superior to the traditional statistical density estimation methods in that neither of the forms of probability function (as in the parametric methods) or the kernel functions (as in the non-parametric methods) is needed to form an a prioriassumption. An example is used to demonstrate that the proposed approach is an effective method for estimating univariate unimodal probability distributions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews DF, Herzberg AM. Data. Springer-Verlag, 1985
Silverman BW. Density estimation for statistics and data analysis. Chapman and Hall, 1986
Brown LD, Hwang JTG. How to approximate a histogram by a normal density. Am Statistician 1993; 47(4): 251–255
Stigler SM. Do robust estimators work with real data? Ann Statistics 1977; 5: 1055–1078
Fisher RA. The use of multiple measurements in taxonomic problems. Ann Eugenics 1936; 7: 179–188
Artikis T, Jerwood D. On the unimodality of present-value distributions. Euro J Operational Res 1991; 52: 107–112
Olshen RA, Savage LJ. A generalized unimodality. J Appl Probability 1970; 7: 21–34
Lukacs E. Characteristic Function, 2nd ed. Griffin, 1970
Archer NP, Wang S. Application of the back propagation neural network algorithm with monotonicity constraints for two-group classification problems. Decision Sci 1993; 24: 60–75
Rumelhart D, McClelland J, PDP Research Group. Parallel Distributed Processing, Vol. 1: Foundations. MIT Press, 1986
Cybenko G. Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems 1989; 2: 303–314
Kawabata T. Generalization effects of k-Neighbour interpolation training. Neural Computation 1991; 3: 409–417
Wang S. Neural network techniques in managerial pattern recognition. Unpublished PhD Dissertation, McMaster University, Hamilton, Canada, 1990
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, S. A neural network method of density estimation for univariate unimodal data. Neural Comput & Applic 2, 160–167 (1994). https://doi.org/10.1007/BF01415012
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01415012