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# negativeBinomial

## negativeBinomial(mu: number, dispersion: number) ðŸ¡’ ranvar, pure function

Returns the negative binomial distribution of mean mu and of dispersion d. The dispersion is the ratio between the variance and the mean: $d = \frac{\sigma^2}{\mu}$. The dispersion should be greater than one.

table T = with
[| as Mu, as Dispersion |]
[|  0.5,  2.0 |]
[|  1.5,  2.0 |]
[|  5.5,  2.0 |]
[|  10.0, 2.0 |]

show table "" a1c4 with
T.Mu
T.Dispersion
negativeBinomial(T.Mu, T.Dispersion)


## negativeBinomial(mu: number, dispersion: number, zeroInflation: number) ðŸ¡’ ranvar, pure function

Overload of the negativeBinomial function, that returns the negative binomial distribution inflated in zero. It is the mixture between a dirac in 0 (with a weight equal to the zeroInflation) and the negative binomial of mean mu and of dispersion d (with a weight equal to 1-zeroInflation). zeroInflation should be in the range $[0, 1]$.

table T = with
[| as Mu, as Dispersion, as ZeroInflation |]
[|  0.5,  2.0, 0.1 |]
[|  1.5,  2.0, 0.2 |]
[|  5.5,  2.0, 0.3 |]
[|  10.0, 2.0, 0.4 |]

show table "" a1c4 with
T.Mu
T.Dispersion
T.ZeroInflation
negativeBinomial(T.Mu, T.Dispersion, T.ZeroInflation)