BETA.DIST
The beta distribution at a value, as a density or a cumulative probability, on 0 to 1 or an interval given.
Group: Statistics. Compatible with DAX.
Syntax
BETA.DIST ( <x>, <alpha>, <beta>, <cumulative> [, <A>] [, <B>] )| Parameter | Type | Description |
|---|---|---|
x | Number | Where the distribution is read: a value from A to B. |
alpha | Number | The first shape parameter, above 0. |
beta | Number | The second shape parameter, above 0. |
cumulative | Boolean | TRUE for the cumulative probability, the chance of a value up to x; FALSE for the density at x. |
A | Number optional | The lower end of x's interval; 0 when left out. |
B | Number optional | The upper end of x's interval; 1 when left out. |
Returns
Number. The beta density at x, or the probability of a value no larger than x.
Remarks
- The beta distribution describes a share or rate that lives between two limits. Alpha and beta set its shape: with both 1 it is flat, so
BETA.DIST ( 0.3, 1, 1, TRUE )is 0.3. - With A and B, x is first moved onto 0 to 1:
BETA.DIST ( 6, 2, 3, TRUE, 2, 12 )equalsBETA.DIST ( 0.4, 2, 3, TRUE ). - A blank x gives BLANK. An x outside A to B, an alpha or beta of 0 or less, or an A that is not below B is an error.
Examples
Density and cumulative probability
EVALUATE
ROW (
"Density", BETA.DIST ( 0.4, 2, 3, FALSE ),
"Cumulative", BETA.DIST ( 0.4, 2, 3, TRUE )
)| Density | Cumulative |
|---|---|
| 1.728 | 0.5248 |
On an interval of its own
The value 6 on the interval 2 to 12 sits where 0.4 sits on 0 to 1, so the two probabilities agree.
EVALUATE
ROW (
"On 0 to 1", BETA.DIST ( 0.4, 2, 3, TRUE ),
"On 2 to 12", BETA.DIST ( 6, 2, 3, TRUE, 2, 12 )
)| On 0 to 1 | On 2 to 12 |
|---|---|
| 0.5248 | 0.5248 |