Hamburger moment problem for powers and products of random variables
| Autor: | Anirban DasGupta, Gwo Dong Lin, Jordan Stoyanov |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Independent and identically distributed random variables Exchangeable random variables Multivariate random variable Applied Mathematics Random element Algebra of random variables Combinatorics Convergence of random variables Sum of normally distributed random variables Proofs of convergence of random variables Applied mathematics Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Journal of Statistical Planning and Inference. 154:166-177 |
| ISSN: | 0378-3758 |
| DOI: | 10.1016/j.jspi.2013.11.002 |
| Popis: | We present new results on the Hamburger moment problem for probability distributions and apply them to characterize the moment determinacy of powers and products of i.i.d. random variables with values in the whole real line. Detailed proofs of all results are given followed by comments and examples. We also provide new and more transparent proofs of a few known results. E.g., we give a new and short proof that the product of three or more i.i.d. normal random variables is moment-indeterminate. The illustrations involve specific distributions such as the double generalized gamma (DGG), normal, Laplace and logistic. We show that sometimes, but not always, the power and the product of i.i.d. random variables (of the same odd ‘order’) share the same moment determinacy property. This is true for the DGG and the logistic distributions. The paper also treats two unconventional types of problems: products of independent random variables of different types and a random power of a given random variable. In particular, we show that the product of Laplace and logistic random variables, the product of logistic and exponential random variables, the product of normal and χ2 random variables, and the random power ZN, where Z ~ N and N is a Poisson random variable, are all moment-indeterminate. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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