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Existence and uniqueness of the maximum likelihood estimator for the two-parameter negative binomial distribution

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  • Aragón, Jorge
  • Eberly, David
  • Eberly, Shelly
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    Abstract

    Given a sample with mean x and second moment s2, Anscombe in 1950 conjectured that the maximum likelihood equations for the two-parameter negative binomial distribution have a unique solution if and only if s2 > x. We give a proof of his conjecture.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 15 (1992)
    Issue (Month): 5 (December)
    Pages: 375-379

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    Handle: RePEc:eee:stapro:v:15:y:1992:i:5:p:375-379

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    Related research

    Keywords: Maximum likelihood estimator negative binomial distribution Newton's method;

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    Cited by:
    1. Ferreri, Carlo, 1997. "On the ML-estimator of the positive and negative two-parameter binomial distribution," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 129-134, April.
    2. Wang, Yining, 1996. "Estimation problems for the two-parameter negative binomial distribution," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 113-114, February.

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