Factorial moment characterizations for certain binomial-type distributions

A W Kemp, C D Kemp

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This article obtains characterizations for the binomial. Grassia I-binomial, (carrier-borne epidemic). and randomized occupancy distributions via their factorial moments. The characierizing condition has the form:

d ln mu([r])'/db = theta(a, b, r)

where mu([r])' denotes the rth factorial moment. a and b are parameters. and theta(a, b: r) is the ratio of two functions linear in r. Given support 0, 1,..., n. then the ratio mu([r])'/mu(2) is an ancillary statistic that is equal, greater than, or less than (n - 1)/n for the three distributions, respectively. The use of the ancillary statistic is demonstrated.

Original languageEnglish
Pages (from-to)3059-3068
Number of pages10
JournalCommunications in Statistics: Theory and Methods
Publication statusPublished - 2004


  • characterization
  • factorial moment
  • binomial distribution
  • Grassia binomial distribution
  • Weiss distribution
  • Carrier-borne epidemic
  • randomized occupancy distribution
  • specified occupancy distribution


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