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Moment Determinacy of Powers and Products of Nonnegative Random Variables

Author

Listed:
  • Gwo Dong Lin

    (Academia Sinica)

  • Jordan Stoyanov

    (Newcastle University)

Abstract

We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on conditions about the distribution itself. For the class of generalized gamma random variables, we show that the power and the product of such variables share the same moment determinacy property. A similar statement holds for half-logistic random variables. Besides answering new questions in this area, we either extend some previously known results or provide new and transparent proofs of existing results.

Suggested Citation

  • Gwo Dong Lin & Jordan Stoyanov, 2015. "Moment Determinacy of Powers and Products of Nonnegative Random Variables," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1337-1353, December.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:4:d:10.1007_s10959-014-0546-z
    DOI: 10.1007/s10959-014-0546-z
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    References listed on IDEAS

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    1. Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
    2. Christian Berg, 2005. "On Powers of Stieltjes Moment Sequences, I," Journal of Theoretical Probability, Springer, vol. 18(4), pages 871-889, October.
    3. Ostrovska, Sofiya & Stoyanov, Jordan, 2010. "A new proof that the product of three or more exponential random variables is moment-indeterminate," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 792-796, May.
    Full references (including those not matched with items on IDEAS)

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