Statistical
Excel 2010
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=GAMMA.DIST()
Returns the gamma distribution. You can use this function to study variables that may have a skewed distribution. The gamma distribution is commonly used in queuing analysis.
Applies To:
Excel for Microsoft 365Excel for Microsoft 365 for MacExcel 2024Excel 2024 for MacExcel 2021Excel 2021 for MacExcel 2019Excel 2016
=GAMMA.DIST(x,alpha,beta,cumulative)
Hover argument names in the table for details.
Output typeStatistical
Popularity5 / 100
VolatileNo
Dynamic ArrayNo
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◧ Arguments
| Argument | Type | Required | Description |
|---|---|---|---|
x |
Number | Required | The value at which you want to evaluate the distribution. |
alpha |
Number | Required | A parameter to the distribution. |
beta |
Number | Required | A parameter to the distribution. If beta = 1, GAMMA.DIST returns the standard gamma distribution. |
cumulative |
Logical | Required | A logical value that determines the form of the function. If cumulative is TRUE, GAMMA.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function. |
▣ Examples
▦ Data
| Cell | Value | Description |
|---|---|---|
A2 |
10.00001131 | Value at which you want to evaluate the distribution |
A3 |
9 | Alpha parameter to the distribution |
A4 |
2 | Beta parameter to the distribution |
A5 |
10.00001131 | Value at which you want to evaluate the distribution |
A6 |
9 | Alpha parameter to the distribution |
A7 |
2 | Beta parameter to the distribution |
Probability density using the x, alpha, and beta values in A2, A3, A4, with FALSE cumulative argument.
=GAMMA.DIST(A2,A3,A4,FALSE)
Result:
0.032639
Cumulative distributuion using the x, alpha, and beta values in A2, A3, A4, with TRUE cumulative argument.
=GAMMA.DIST(A2,A3,A4,TRUE)
Result:
0.068094
§ Remarks
- If x, alpha, or beta is nonnumeric, GAMMA.DIST returns the #VALUE! error value.
- If x < 0, GAMMA.DIST returns the #NUM! error value.
- If alpha ≤ 0 or if beta ≤ 0, GAMMA.DIST returns the #NUM! error value.
- The equation for the gamma probability density function is: The standard gamma probability density function is:
- When alpha = 1, GAMMA.DIST returns the exponential distribution with:
- For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMA.DIST returns (1 - CHISQ.DIST.RT(x)) with n degrees of freedom.
- When alpha is a positive integer, GAMMA.DIST is also known as the Erlang distribution.
✦ Tips
- The equation for the gamma probability density function is: The standard gamma probability density function is:
- When alpha = 1, GAMMA.DIST returns the exponential distribution with:
- For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMA.DIST returns (1 - CHISQ.DIST.RT(x)) with n degrees of freedom.
- When alpha is a positive integer, GAMMA.DIST is also known as the Erlang distribution.
⚠ Common Errors
#VALUE!
If x, alpha, or beta is nonnumeric, GAMMA.DIST returns the #VALUE! error value.
Fix: برای هر سه آرگومان مقدار عددی وارد کنید.
#NUM!
If x < 0, GAMMA.DIST returns the #NUM! error value. If alpha ≤ 0 or if beta ≤ 0, GAMMA.DIST returns the #NUM! error value.
Fix: Correct the input value
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