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Invariant expectation values in the sampling of discrete frequency distributions

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  • Rossi, Paolo

Abstract

The general relationship between an arbitrary frequency distribution and the expected value of the frequency distributions of its samples is discussed. A wide set of measurable quantities (“invariant moments”) whose expected value does not in general depend on the size of the sample is constructed and illustrated by applying the results to the Ewens sampling formula. Invariant moments are especially useful in the sampling of systems characterized by the absence of an intrinsic scale. Distribution functions that may parametrize the samples of scale-free distributions are considered and their invariant expectation values are computed. The conditions under which the scaling limit of such distributions may exist are described.

Suggested Citation

  • Rossi, Paolo, 2014. "Invariant expectation values in the sampling of discrete frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 177-186.
    • Handle: RePEc:eee:phsmap:v:394:y:2014:i:c:p:177-186
    DOI: 10.1016/j.physa.2013.09.056
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    1. Joseph Hilbe, 1994. "Negative binomial regression," Stata Technical Bulletin, StataCorp LLC, vol. 3(18).
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