Model to be choose if Poisson distribution mean and variance are not the same, say If mean is greater than variance or variance is greater than mean?

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Model to be chosen if Poisson distribution mean and variance are not the same, say If mean is greater than variance or variance is greater than mean?

poisson data-modeling statistics
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If you only have mean and variance, and they are not equal, obviously you have to try two-parametric discrete distribution. From the top of my head:

  • Binomial
  • Negative binomial
  • Hypergeometric distribution
  • Negative Hypergeometric
  • Compound distributions like Gamma-Poisson mix
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