Statnote 37 : the negative binomial distribution

Anthony Hilton, Richard Armstrong

Research output: Contribution to specialist publicationArticle

Abstract

An organism living in water, and present at low density, may be distributed at random and therefore, samples taken from the water are likely to be distributed according to the Poisson distribution. The distribution of many organisms, however, is not random, individuals being either aggregated into clusters or more uniformly distributed. By fitting a Poisson distribution to data, it is only possible to test the hypothesis that an observed set of frequencies does not deviate significantly from an expected random pattern. Significant deviations from random, either as a result of increasing uniformity or aggregation, may be recognized by either rejection of the random hypothesis or by examining the variance/mean (V/M) ratio of the data. Hence, a V/M ratio not significantly different from unity indicates a random distribution, greater than unity a clustered distribution, and less then unity a regular or uniform distribution . If individual cells are clustered, however, the negative binomial distribution should provide a better description of the data. In addition, a parameter of this distribution, viz., the binomial exponent (k), may be used as a measure of the ‘intensity’ of aggregation present. Hence, this Statnote describes how to fit the negative binomial distribution to counts of a microorganism in samples taken from a freshwater environment.
LanguageEnglish
Pages37-39
Number of pages3
Volume15
Specialist publicationMicrobiologist
Publication statusPublished - Jun 2014

Fingerprint

organisms
water
microorganisms
sampling
binomial distribution
testing
cells
Poisson distribution

Keywords

  • data analysis methods
  • negative binomial distribution
  • clustering analysis
  • freshwater environments

Cite this

Hilton, Anthony ; Armstrong, Richard. / Statnote 37 : the negative binomial distribution. In: Microbiologist. 2014 ; Vol. 15. pp. 37-39.
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Statnote 37 : the negative binomial distribution. / Hilton, Anthony; Armstrong, Richard.

In: Microbiologist, Vol. 15, 06.2014, p. 37-39.

Research output: Contribution to specialist publicationArticle

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