Gamma Distribution |
(continuous probability dist for equations) |
Usage: |
GammaDist (x, a, b) |
Definition: |
x^( a-1) exp(-x/ b) / (gamma(a) b ^ a) = exp[(a-1)log(x) - x/ b - log(gamma(a)) - a log(b)] |
Parameters: |
a is shape b is scale |
Required: |
a > 0 b > 0 |
Support: |
x ³ 0 |
Moments: |
m = a b s = b sqrt (a) g1 = 2 / sqrt (a) b2 = 3 + 6 / a |
If events occur by a = 4 && typeof(BSPSPopupOnMouseOver) == 'function') BSPSPopupOnMouseOver(event);" class="BSSCPopup" onclick="BSSCPopup('X_PU_Poisson_process.htm');return false;">Poisson process, then the time required for the occurrence of a events is described by the gamma distribution (where b is the average time between events).
For a = 1, this is the exponential distribution with l = 1 / b. For b = 2, this is the chi-square distribution with degrees of freedom n = 2 a.
The Erlang distribution is a special case of the gamma distribution in which b = 1 and a = n (which is an integer).