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A New Convexity-Based Inequality, Characterization of Probability Distributions, and Some Free-of-Distribution Tests
- Source :
- Journal of Mathematical Sciences. 251:38-45
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- A goal of the paper is to prove new inequalities connecting some functionals of probability distribution functions. These inequalities are based on the strict convexity of functions used in the definition of the functionals. The starting point is the paper “Cramer–von Mises distance: probabilistic interpretation, confidence intervals and neighborhood of model validation” by Ludwig Baringhaus and Norbert Henze. The present paper provides a generalization of inequality obtained in probabilistic interpretation of the Cramer–von Mises distance. If the equality holds there, then a chance to give characterization of some probability distribution functions appears. Considering this fact and a special character of the functional, it is possible to create a class of free-of-distribution two sample tests.
- Subjects :
- Statistics and Probability
Class (set theory)
Generalization
Applied Mathematics
General Mathematics
Probability (math.PR)
010102 general mathematics
Probabilistic logic
01 natural sciences
Convexity
010305 fluids & plasmas
Interpretation (model theory)
Character (mathematics)
Distribution (mathematics)
0103 physical sciences
FOS: Mathematics
Probability distribution
Applied mathematics
60E10, 62E10
0101 mathematics
Mathematics - Probability
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 251
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi.dedup.....34a698296fc072ee59313c6facbe2f0b