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https://hdl.handle.net/10316/102687
Title: | The 123 theorem of Probability Theory and Copositive Matrices | Authors: | Kovacec, Alexander Moreira, Miguel M. R. Martins, David P. |
Keywords: | probabilistic inequalities; copositivity; integral inequality | Issue Date: | 2014 | Serial title, monograph or event: | Special Matrices | Volume: | 2 | Issue: | 1 | Abstract: | Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(‖X − Y‖ b) c Prob(‖X − Y‖ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality for monotone functions. | URI: | https://hdl.handle.net/10316/102687 | ISSN: | 2300-7451 | DOI: | 10.2478/spma-2014-0016 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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