Abstract
For a random sample from a population having a finite k-th moment, it is shown that the constancy of regression of polynomial statistics of order k in the mean implies that all higher moments exist and are uniquely determined by the first k moments. This result is utilized to give a moment's approach to some characterization results.
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Alzaid, A.A. A moment's approach to some characterization problems. Ann Inst Stat Math 42, 281–285 (1990). https://doi.org/10.1007/BF00050837
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DOI: https://doi.org/10.1007/BF00050837