Mathematics and Statistics Vol. 6(4), pp. 50 - 60
DOI: 10.13189/ms.2018.060402
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Probabilities Obtained by Means of Hyperhomographies into a Quadruple Random Quantity

Pierpaolo Angelini ^*
Department of Statistical Sciences, Sapienza University of Rome, Italy

ABSTRACT

I realized that it is possible to construct an original and well-organized theory of multiple random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. A very important point relevant to such a construction is consequently treated in this paper by showing that a coherent prevision of a bivariate random quantity coincides with the notion of -product of two vectors while a coherent prevision of a quadruple random quantity coincides with the notion of -product of two affine tensors. Metric properties of the notion of -product mathematically characterize both the notion of coherent prevision of a generic bivariate random quantity and the notion of coherent prevision of a generic quadruple random quantity. Coherent previsions of bivariate and quadruple random quantities can be used in order to obtain fundamental metric expressions of bivariate and quadruple random quantities.

KEYWORDS
Hyperhomography, Translation, Affine Tensor, Antisymmetric Tensor, -product, -norm

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Pierpaolo Angelini , "Probabilities Obtained by Means of Hyperhomographies into a Quadruple Random Quantity," Mathematics and Statistics, Vol. 6, No. 4, pp. 50 - 60, 2018. DOI: 10.13189/ms.2018.060402.

(b). APA Format:
Pierpaolo Angelini (2018). Probabilities Obtained by Means of Hyperhomographies into a Quadruple Random Quantity. Mathematics and Statistics, 6(4), 50 - 60. DOI: 10.13189/ms.2018.060402.