Some inequalities for characteristic density functions with bounded variation (Q700467)
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scientific article; zbMATH DE number 1818146
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some inequalities for characteristic density functions with bounded variation |
scientific article; zbMATH DE number 1818146 |
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Some inequalities for characteristic density functions with bounded variation (English)
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21 October 2002
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Let \(p(x)\) be a probability distribution with the bounded variation \(V(p)\). Then its characteristic function \(f(t)\) satisfies the following inequalities \[ |f(t)|\leq\sin(t/V(p))/(t/V(p)),\;|t|\leq\pi V(p),\quad\text{and}\quad |f(t)|\leq V(p)/t,\;t\neq 0. \]
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probability distribution
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vertex
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variation
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