BETA.INV
The value at which the beta distribution's cumulative probability is the one given.
Group: Statistics. Compatible with DAX.
Syntax
BETA.INV ( <probability>, <alpha>, <beta> [, <A>] [, <B>] )| Parameter | Type | Description |
|---|---|---|
probability | Number | The cumulative probability wanted, strictly between 0 and 1. |
alpha | Number | The first shape parameter, above 0. |
beta | Number | The second shape parameter, above 0. |
A | Number optional | The lower end of the result's interval; 0 when left out. |
B | Number optional | The upper end of the result's interval; 1 when left out. |
Returns
Number. The x at which BETA.DIST with the same parameters reaches the probability.
Remarks
- It is the inverse of
BETA.DIST: feeding its answer back gives the probability again, to the last digits. - A probability of 0 or 1 or beyond, an alpha or beta of 0 or less, or an A not below B is an error.
- A common use is an interval for a rate. With 30 successes in 100 trials and a flat prior,
BETA.INV ( 0.025, 31, 71 )andBETA.INV ( 0.975, 31, 71 )bound the rate with 95 % probability.
Examples
The median, and back
EVALUATE
ROW (
"Median", BETA.INV ( 0.5, 2, 3 ),
"Back", BETA.DIST ( BETA.INV ( 0.5, 2, 3 ), 2, 3, TRUE )
)| Median | Back |
|---|---|
| 0.38572756813239 | 0.5 |
Three quantiles of one distribution
EVALUATE
VAR Shares = DATATABLE ( "p", DOUBLE, { { 0.1 }, { 0.5 }, { 0.9 } } )
RETURN
ADDCOLUMNS ( Shares, "Beta(2, 5)", BETA.INV ( [p], 2, 5 ) )| p | Beta(2, 5) |
|---|---|
| 0.1 | 0.0925952589131288 |
| 0.5 | 0.26444998329566 |
| 0.9 | 0.510316306551492 |
A 95 % interval for a rate of 30 in 100
EVALUATE
ROW (
"Lower", BETA.INV ( 0.025, 31, 71 ),
"Upper", BETA.INV ( 0.975, 31, 71 )
)| Lower | Upper |
|---|---|
| 0.218978726304034 | 0.396147128647689 |