Syntax
GAMMA.DIST(x, alpha, beta, cumulative)
| Parameter | Description |
|---|---|
| x | Parameter of the GAMMA.DIST function. |
| alpha | Parameter of the GAMMA.DIST function. |
| beta | Parameter of the GAMMA.DIST function. |
| cumulative | Parameter of the GAMMA.DIST function. |
Examples
Probability of completing within 5 hours
Formula
=GAMMA.DIST(5, 3, 1.5, TRUE)
Returns ~0.5543. If the total processing time follows a gamma distribution with shape=3 and scale=1.5 (sum of 3 exponential stages), there is about a 55% chance of finishing within 5 hours.
Insurance claim size probability
Formula
=GAMMA.DIST(10000, 2, 5000, TRUE)
Returns ~0.5940. About 59% of claims are expected to be $10,000 or less under this gamma model.
PDF for plotting
Formula
=GAMMA.DIST(3, 2, 1, FALSE)
Returns ~0.1494. The probability density at x=3 for a gamma distribution with alpha=2 and beta=1.
Common Errors
#NUM!
x must be non-negative, and both alpha (shape) and beta (scale) must be positive.
#VALUE!
Occurs when arguments are non-numeric.
Tips
Shape and scale parameters
Alpha (shape) determines the number of 'stages' and beta (scale) determines the time scale. Mean = alpha * beta, variance = alpha * beta^2.
Special cases
Gamma with alpha=1 is the exponential distribution. Gamma with alpha=k/2 and beta=2 is the chi-squared distribution with k degrees of freedom.
Modeling multiple stages
If a process has k identical independent stages each taking exponential time with mean beta, the total time follows a gamma distribution with shape=k and scale=beta.
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