Equivalence between distribution functions and probability measures on a lots

Constructive Equivalence Relations on Computable Probability Measures

A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computabl...

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 ...

On the Concavity of Multivariate Probability Distribution Functions on the Concavity of Multivariate Probability Distribution Functions

We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems.

On the Distribution of Natural Probability Functions

A Note on the Coherence between Probability and Possibility Measures

Mamoni Dhar Assistant Professor Science College, Kokrajhar Kokrajhar-783370, India 1st Author ABSTRACT In this article, we intend to revisit the coherence established between possibility and probability from some functions which are density functions and would like to draw attention of the fact that since a possibility distribution of a normal fuzzy number can be expressed as two distribution f...