The Generalized Omega Function and Its Connection with Some Probability Distributions

Jónás, Tamás; Bakouch, Hassan S.

doi:10.1007/s00009-022-02184-2

Cited by 1 publication

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and let its probability density function [17,19,20] p : I m → R ++ be continuous. Then the probability distribution function [17,23] of the random variable µ is…”

Section: Applications In Probability Theorymentioning

confidence: 99%

“…The research tools of the paper include the functional analysis, discrete mathematics, probability [17,19,20,[22][23][24][25][26][27], convex geometry [28], linear algebra [2], inequality and the mean value [15,16,18,27,[29][30][31][32][33][34] theories, especially the mean value theory. The research methods of the paper are based on the mathematical induction [2,17,18,32], reorder method [2] and the dimension reduction method [32].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev-Jensen-type inequalities and their applications in probability theory with surround system

Wen

Han

Yuan

2023

Preprint

View full text Add to dashboard Cite

This paper will establish Chebyshev-Jensen-type inequalities which involving the Chebyshev products as follows:\[\langle X^{1}, X^{2}, \ldots, X^{m}\rangle_{\chi}\geq \left[ X^{1}, X^{2}, \ldots, X^{m}\right]_{\chi}\geq \chi\left( \overline{X^{1}}, \overline{X^{2}}, \ldots, \overline{X^{m}}\right)\]and\[\langle f_{1}, f_{2}, \ldots, f_{m}\rangle_{\chi}\geq \left[f_{1}, f_{2}, \ldots,f_{m}\right]_{\chi}\geq \chi\left( \overline{f_{1}}, \overline{f_{2}}, \ldots, \overline{f_{m}}\right),\]as well as display their applications in probability theory and surround system, especially, the observation angles inequalities are obtained as follows:\[1\geq \frac{1}{n}\sum_{i=1}^{n}P\left(R_{i}\right)\geq \frac{1}{n^{m}}\sum_{1\leq i_{1},\ldots,i_{m}\leq n}P(R_{i_{1},\ldots,i_{m}})\geq\left(\frac{2}{n}\right)^{m+|\alpha|}.\]The research methods of the paper are based on the mathematical induction, reorder method and the dimension reduction method. 2010 MSC: 26D15, 26E60, 51K05, 52A40

show abstract

“…and let its probability density function [17,19,20] p : I m → R ++ be continuous. Then the probability distribution function [17,23] of the random variable µ is…”

Section: Applications In Probability Theorymentioning

confidence: 99%