loglikelihood.negativeBinomial

loglikelihood.negativeBinomial, function

def autodiff pure loglikelihood.negativeBinomial(
    mean: number,
    dispersion: number,
    k: number): number
def autodiff pure loglikelihood.negativeBinomial(
    mean: number,
    dispersion: number,
    zeroInflation: number,
    k: number): number

Returns the log-likelihood of observing k under a negative binomial distribution, optionally with zero inflation.

• mean: mean of the distribution, must be positive.
• dispersion: dispersion, must be >= 1.
• zeroInflation: extra probability mass at zero, in [0, 1].
• k: observation, must be a non-negative integer.

Examples

table T = with
  [| as Mean, as Dispersion, as K |]
  [| 2, 1.5, 3 |]
  [| 4, 2.0, 0 |]

T.LL = loglikelihood.negativeBinomial(T.Mean, T.Dispersion, T.K)

show table "Negative binomial" with
  T.Mean
  T.Dispersion
  T.K
  T.LL

This produces the following table:

table T = with
  [| as Mean, as Dispersion, as ZeroInflation, as K |]
  [| 2, 1.5, 0.2, 0 |]
  [| 2, 1.5, 0.2, 3 |]

T.LL = loglikelihood.negativeBinomial(
  T.Mean, T.Dispersion, T.ZeroInflation, T.K)

show table "Zero inflated" with
  T.K
  T.LL

This produces the following table:

See also

• Regress distribution parameters with autodiff