When Do the Moments Uniquely Identify a Distribution

Carlos A. Coelho (), Rui P. Alberto and Luís M. Grilo
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Carlos A. Coelho: NOVA University of Lisbon, Mathematics Department and NOVA Math, NOVA School of Science and Technology
Rui P. Alberto: NOVA University of Lisbon, NOVA Math, NOVA School of Science and Technology
Luís M. Grilo: NOVA University of Lisbon, NOVA Math, NOVA School of Science and Technology

A chapter in Directional and Multivariate Statistics, 2025, pp 239-256 from Springer

Abstract: Abstract The authors establish when do the moments $$E(X^h)$$ E ( X h ) , for h in some subset C of $$\mathbb R$$ R , uniquely identify the distribution of any positive random variable X, that is, when is $$x^h$$ x h a separating function. The simple necessary and sufficient condition is shown to be related with the existence of the moment generating function of the random variable $$Y=log X$$ Y = l o g X . The subset C of $$\mathbb R$$ R is thus the set of values of h for which the moment generating function of Y is defined. Examples of random variables characterized in this way by the set of their h-th moments are given.

Keywords: Moment problem; Identifiability; Separating functions; Log-normal distribution; F distribution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-981-96-2004-3_13

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