On the moment determinacy of products of non-identically distributed random variables

• Autorzy: Lin, G. D. , Stoyanov, J.
• Języki publikacji: EN

Abstrakty

EN

We show first that there are intrinsic relationships among different conditions, old and recent, which lead to some general statements in both the Stieltjes and the Hamburger moment problems. Then we describe checkable conditions and prove new results about the moment (in)determinacy for products of independent and non-identically distributed random variables. We treat all three cases: when the random variables are nonnegative (Stieltjes case), when they take values in the whole real line (Hamburger case), and the mixed case. As an illustration we characterize the moment determinacy of products of random variables whose distributions are generalized gamma or double generalized gamma all with distinct shape parameters. Among other corollaries, the product of two independent random variables, one exponential and one inverse Gaussian, is moment determinate, while the product is moment indeterminate for the cases: one exponential and one normal, one chi-square and one normal, and one inverse Gaussian and one normal.

Słowa kluczowe

EN

product of random variables; Stieltjes moment problem; Hamburger moment problem; Cramér’s condition; Carleman’s condition; Krein’s condition; Hardy’s condition

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 1
• Strony: 21--33
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Lin, G. D.

• Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, ROC,

autor

Stoyanov, J.

• School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK,

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).