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The 123 theorem of Probability Theory and Copositive Matrices

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Kovačec A., Moreira M. M. R., Martins D. P.

Special Matrices

2014

tom 2

nr 1

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.

Ograniczanie wyników

1 Special Matrices

1 Kovačec A.

1 Martins D. P.

1 Moreira M. M. R.

1 2014

Wyniki wyszukiwania

The 123 theorem of Probability Theory and Copositive Matrices