Principal Components of the Pareto Distribution

Cuadras, Carles M.; Lahlou, Younes

doi:10.1007/978-94-017-0061-0_6

Cited by 6 publications

(3 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It extends some results by Cuadras [6][7][8], Cuadras and Fortiana [12], Cuadras and Lahlou [14,15] and Cuadras et al [13,11]. Finally some series of constants are obtained as a by-product.…”

Section: Introductionmentioning

confidence: 51%

Eigenanalysis on a bivariate covariance kernel

Cuadras

2008

Journal of Multivariate Analysis

Self Cite

View full text Add to dashboard Cite

Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative distribution function is used. Some bounds for the trace of the kernel and some inequalities for a continuous random variable concerning a function and its derivative are obtained. We also obtain relations to diagonal expansions and canonical correlation analysis and, as a by-product, series of constants for some particular distributions.

show abstract

Section: Introductionmentioning

confidence: 51%

Eigenanalysis on a bivariate covariance kernel

Cuadras

2008

Journal of Multivariate Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another class of Dynkin systems occurs in so-called marginal scenarios [ 32 ]. Marginal scenarios are settings in which marginal probability distributions for a subset of a set of random variables are given, but not the entire joint distribution.…”

Section: What Is a (Pre-)dynkin System?mentioning

confidence: 99%

“…In machine learning, each marginal scenario gets equipped an own probability space, i.e., an own context (cf. [ 3 , 32 ]).) Again, as for pre-Dynkin systems and finitely additive probabilities, the question of embedding Dynkin probability spaces into classical probability spaces arises.…”

Section: Appendix A1 Compatibility Structurementioning

confidence: 99%

Systems of Precision: Coherent Probabilities on Pre-Dynkin Systems and Coherent Previsions on Linear Subspaces

Derr,

Williamson

2023

Entropy

View full text Add to dashboard Cite

In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a lower and upper probability form a so-called (pre-)Dynkin system. Interestingly, there are several settings, ranging from machine learning on partial data over frequential probability theory to quantum probability theory and decision making under uncertainty, in which, a priori, the probabilities are only desired to be precise on a specific underlying set system. Here, (pre-)Dynkin systems have been adopted as systems of precision, too. We show that, under extendability conditions, those pre-Dynkin systems equipped with probabilities can be embedded into algebras of sets. Surprisingly, the extendability conditions elaborated in a strand of work in quantum probability are equivalent to coherence from the imprecise probability literature. On this basis, we spell out a lattice duality which relates systems of precision to credal sets of probabilities. We conclude the presentation with a generalization of the framework to expectation-type counterparts of imprecise probabilities. The analogue of pre-Dynkin systems turns out to be (sets of) linear subspaces in the space of bounded, real-valued functions. We introduce partial expectations, natural generalizations of probabilities defined on pre-Dynkin systems. Again, coherence and extendability are equivalent. A related but more general lattice duality preserves the relation between systems of precision and credal sets of probabilities.

show abstract

Distance-based Multivariate Two Sample Tests

Cuadras

Fortiana

2004

Statistics for Industry and Technology

View full text Add to dashboard Cite

Principal Components of the Pareto Distribution

Cited by 6 publications

References 6 publications

Eigenanalysis on a bivariate covariance kernel

Eigenanalysis on a bivariate covariance kernel

Systems of Precision: Coherent Probabilities on Pre-Dynkin Systems and Coherent Previsions on Linear Subspaces

Distance-based Multivariate Two Sample Tests

Contact Info

Product

Resources

About