Non-Additive Probability Measures with Interval Density Functions

Interval-Valued Probability Measures

The purpose of this paper is propose a simple de…nition of an interval-valued probability measure and to examine some of the implications of this de…nition. This de…nition provides a method for characterizing certain types of imprecise probabilities. We develop some properties of this de…nition and propose a de…nition of integration with respect to it. We show that this de…nition is a generaliz...

Non-additive probability

Comprehensive Survey on Distance / Similarity Measures between Probability Density Functions

Distance or similarity measures are essential to solve many pattern recognition problems such as classification, clustering, and retrieval problems. Various distance/similarity measures that are applicable to compare two probability density functions, pdf in short, are reviewed and categorized in both syntactic and semantic relationships. A correlation coefficient and a hierarchical clustering ...

Eecient Non-parametric Estimation of Probability Density Functions

Accurate and fast estimation of probability density functions is crucial for satisfactory computational performance in many scientiic problems. When the type of density is known a priori, then the problem becomes statistical estimation of parameters from the observed values. In the non-parametric case, usual estimators make use of kernel functions. If X j ; j = 1; 2; : : : ; n is a sequence of ...

Non-additive measures and integrals

There is presented a short overview on some results related the theory of non-additive measures and the corresponding integrals occurring in several important applications.