Moment determinacy of powers, products and other transforms of nonnegative random variables

We study the moment determinacy of nonlinear (Box-Cox) transformations of random variables. We establish new criteria for moment (in)determinacy and apply them to powers and products of nonnegative random variables. In particular, we show that the power and the product (of the same ‘order’) of generalized gamma random variables, both share the same moment determinacy property. Similar statement holds also for half-logistic random variables. The moment (in)determinacy of other transforms of random variables are also studied. We prove new results answering new questions in this area. In a few cases we either extend previously known results or provide new proofs to existing results. Related topics are briefly discussed. 2010 Mathematics Subject Classification: 60E05, 44A60, 33B15, 62G30

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