Negative Binomial Distribution |
(discrete probability dist. for equations) |
Usage: |
NegBinomialDist (k, n, p) |
Definition: |
binomial (n+k-1, k) p^n (1-p)^k where binomial is the binomial coefficient. |
Required: |
0 ⋜ n 0 < p ⋜ 1 k and n are integers
|
Support: |
0 ⋜ k |
Moments: |
μ = n (1-p) / p σ^2 = n (1-p) / p^2 γ1 = (2 - p) / sqrt (n (1 - p)) β2 = 3 + [p^2 + 6 (1-p)] / (n (1 - p)) |
This is the distribution of the number of failures that occur in a sequence of trials before n successes have occurred, in a Bernoulli process (independent trials, with outcomes labeled "success" or "failure", and constant probability p of success).
The limit of a negative binomial distribution as n → ∞, (1-p) → 0, n(1-p) → λ, is a Poisson distribution with parameter λ.
If n = 1, then this distribution is just the geometric distribution.
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