Abstract
Under various conditions, several authors have given an affirmative answer to Problem 234 in Statistica Neerlandica (Gill [Gil89]): Distributions with a decreasing probability density function have positive centered moments. This problem is discussed in Section 7.1. In Section 7.2 several mean preserving representations are proved; one of them (Theorem 7.2.12) will be used to prove the positivity of functional moments (slantedness) for unimodal probability measures. In Section 7.3 we first indicate several ‘nice’ function sets as well as key tools for proving slantedness. Then a slantedness result (Theorem 7.3.3) is proved. Signed moments are also considered. A brief discussion on the concept of slantedness closes this section.
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© 1997 Springer Science+Business Media Dordrecht
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Bertin, E.M.J., Cuculescu, I., Theodorescu, R. (1997). Positivity of functional moments. In: Unimodality of Probability Measures. Mathematics and Its Applications, vol 382. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8808-9_7
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DOI: https://doi.org/10.1007/978-94-015-8808-9_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4769-4
Online ISBN: 978-94-015-8808-9
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