Some inequalities for characteristic functions |
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Authors: | Chin-Yuan Hu |
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Affiliation: | a Department of Business Education, National Changhua University of Education, Changhua 50058, Taiwan, ROC b Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, ROC |
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Abstract: | In a recent paper, Matysiak and Szablowski [V. Matysiak, P.J. Szablowski, Theory Probab. Appl. 45 (2001) 711-713] posed an interesting conjecture about a lower bound of real-valued characteristic functions. Under a suitable moment condition on distributions, we prove the conjecture to be true. The unified approach proposed here enables us to obtain new inequalities for characteristic functions. We also show by example that the improvement in the bounds is significant if more information about the distribution is available. |
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Keywords: | Inequality Characteristic function Differential inequality Linear regression of a random variable |
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