Inequalities of the Chebyshev type based on pseudo-integrals.

This paper presents the Chebyshev type of pseudo-integral inequalities, with the particular emphasis on the g -semirings. With the suitable choice of the generator g , the pseudo-expectation and pseudo-moments exist for the Cauchy distribution (in general case the standard expectation and moments for the Cauchy distribution are not defined). The computation of the pseudo-expectation for the Cauchy distribution and some examples that illustrate the applicability of the introduced generalization are also given in the paper. [ABSTRACT FROM AUTHOR]