Negative Binomial Distribution |
(discrete probability dist. for equations) |
Usage: |
NegBinomialDist (k, n, p) |
Definition: |
binomial (n+k-1, k) p^n (1-p)^k |
Required: |
0 £ n 0 < p £ 1 k and n are integers
|
Support: |
0 £ k |
Moments: |
m = n (1-p) / p s^2 = n (1-p) / p^2 g1 = (2 - p) / sqrt (n (1 - p)) b2 = 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 = 4 && typeof(BSPSPopupOnMouseOver) == 'function') BSPSPopupOnMouseOver(event);" class="BSSCPopup" onclick="BSSCPopup('X_PU_Bernoulli_process.htm');return false;">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) ® l, is a Poisson distribution with parameter l.
If n = 1, then this distribution is just the geometric distribution.