B.5 A hierarchy of discrete distributions
Table B.1 indicates which distributions are special or limiting cases of others. For the special cases, one parameter is set equal to a constant to create the special case. For the limiting cases, two parameters go to infinity or zero in some special way.
Table B.1 Hierarchy of discrete distributions.
| Distribution | Is a special case of | Is a limiting case of |
| Poisson | ZM Poisson | Negative binomial, Poisson–binomial, Poisson–inv. Gaussian, Polya–Aeppli, Neyman–A |
| ZT Poisson | ZM Poisson | ZT negative binomial |
| ZM Poisson | ZM negative binomial | |
| Geometric | Negative binomial ZM geometric | Geometric–Poisson |
| ZT geometric | ZT negative binomial | |
| ZM geometric | ZM negative binomial | |
| Logarithmic | ZT negative binomial | |
| ZM logarithmic | ZM negative binomial | |
| Binomial | ZM binomial | |
| Negative binomial | ZM negative binomial | Poisson-ETNB |
| Poisson–inverse Gaussian | Poisson–ETNB | |
| Polya–Aeppli | Poisson–ETNB | |
| Neyman–A | Poisson–ETNB |
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