## Selected Topics in Characteristic FunctionsThe series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students. |

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### Contents

Inequalities | 67 |

A Examples | 260 |

B Some characteristic functions | 282 |

Unsolved problems | 331 |

351 | |

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### Common terms and phrases

absolutely continuous distribution acteristic bounded variation ch.f char charac characteristic func characteristic function f(t conditions of Theorem consider converges COROLLARY corresponding characteristic functions corresponding distribution cosx covariance matrix Csorgo Denote density estimation density function p(x dF(x differentiable discrete unimodal distribution F distribution function F(x empirical characteristic function empirical distribution function estimator pn(x example exists a characteristic Feuerverger finite fn(t function with characteristic hence implies inequality integer integrable interval J-oo kernel estimator Lebesgue measure Lemma Let F(x Let the conditions Let us prove lim sup m-dimensional multi-dimensional multivariate non-negative normal distribution obtain oo oo parameter positive integer positive numbers probability density function proof of Theorem random variable random vector right-hand side satisfying conditions satisfying the conditions sequence sinx teristic function test statistic tic functions tion un(t underlying distribution uniform distribution unimodal distribution univariate Ushakov values virtue of Theorem

### Popular passages

Page 340 - Heathcote, CR ( 1972). A test of goodness of fit for symmetric random variables. Austral. J. Statist. 14, 172-181.

Page 339 - FANG, KT, KOTZ, S. and NG, KW (1989). Symmetric Multivariate and Related Distributions, London and New York: Chapman and Hall.

Page 336 - Binmore, KG, and Stratton, HH (1969). A note on characteristic functions. Ann. Math. Statist. 40, 303-307.