Some properties of Choquet integral based probability functions

Vicenç Torra


The Choquet integral permits us to integrate a function with respect to a non-additive measure. When the measure is additive it corresponds to the Lebesgue integral. This integral was used recently to define families of probability-density functions. They are the exponential family of Choquet integral (CI) based class-conditional probability-density functions, and the exponential family of Choquet– Mahalanobis integral (CMI) based class-conditional probability-density functions. The latter being a generalization of the former, and also a generalization of the normal distribution.

In this paper we study some properties of these distributions, and study the application of a few normality tests.


Choquet integral; non-additive measures; Choquet integral based probability functions; normality tests

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ISSN 1406–2283 (print)
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