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Study on Moment-(in)determinacy in Stieltjes Moment Problem

Jie Mi


The classic moment problem is to determine whether or not the distribution function of a given random variable is uniquely determined by its moment sequence. It is called the Stieltjes moment problem if the given random variable is non-negative. This article gives some new methods for checking the moment-(in)determinacy in terms of the probability density function or failure rate function of a given random variable in the Stieltjes case. Focus is on the Hardy's condition which guarantees the moment-determinacy of a given distribution function. Closure properties of moment-(in)determinacy and the Hardy's condition are also explored.


Moment problem, Hardy's condition, Failure rate, Dominance.

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