Statistical Papers

, Volume 41, Issue 2, pp 159–171 | Cite as

Asymptotic estimators of the sample size in a record model

  • Erhard Cramer


The connection between Stirling numbers of the first kind and records is well-known. Applying this relationship, we derive bounds for the maximum likelihood estimator of the sample size based on the number of observed records. The proof proceeds by a remarkable expression of the mode of the unsigned Stirling numbers of the the first kind due to Hammersley. Moreover, this representation of the mode leads to an accurate approximation of the maximum likelihood estimator.


Lower records Estimation Sample size Stirling numbers of the first kind Unimodality 


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Copyright information

© Springer-Verlag 2000

Authors and Affiliations

  1. 1.Institut für MathematikUniversität OldenburgOldenburgGermany

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