Investment Studio > Expressions > Functions > Statistical > GAMMADIST
float gammadist(float x, float alpha, float beta, boolean cumulative)
Returns the gamma probability function.
x must be >= 0.
alpha and beta must be > 0.
If cumulative = TRUE, the CDF (Cumulative Distribution Function) is returned (equal to the probability that x is >= a stochastic variable with exponential distribution); otherwise, the PDF (Probability Density Function) is returned.
Mathematically, the gamma PDF is
| xa-1 e-x/b | |
| f(x, a, b) = | ¾¾¾¾ |
| ba G(a) |
and the CDF is
| x | ||
| F(x, a, b) = | ó | f(u, a, b) du |
| ô | ||
| õ | ||
| 0 |
For integer a > 0, the gamma distribution is the distribution of the sum of a independent, exponentially distributed stochastic variables with l = 1 / b (see expondist), also known as the Erlang distribution.
Setting a = 1 yields the exponential distribution with l = 1 / b. Also,
gammadist(x, n/ 2, 2, TRUE) = 1 - chidist(x, n, TRUE)
The standard gamma distribution described in most statistical texts is obtained by setting b = 1.
Example
=gammadist(9, 8, 3, FALSE)
returns 0.00720134381749461.
=gammadist(9, 8, 3, TRUE)
returns 0.0119045038561503.