EXPON.DIST
The exponential distribution at a value, as a density or a cumulative probability.
Group: Statistics. Compatible with DAX.
Syntax
EXPON.DIST ( <x>, <lambda>, <cumulative> )| Parameter | Type | Description |
|---|---|---|
x | Number | The waiting time or distance, 0 or more. |
lambda | Number | The rate: events per unit of x, above 0. |
cumulative | Boolean | TRUE for the chance that the wait is at most x; FALSE for the density at x. |
Returns
Number. The exponential density at x, or the probability of a wait no longer than x.
Remarks
- The cumulative form is 1 − e^(−lambda × x). The mean wait is 1 / lambda.
- A blank x gives BLANK. A negative x, or a lambda of 0 or less, is an error.
Examples
Density and cumulative probability
EVALUATE
ROW (
"Density", EXPON.DIST ( 0.5, 2, FALSE ),
"Cumulative", EXPON.DIST ( 0.5, 2, TRUE )
)| Density | Cumulative |
|---|---|
| 0.735758882342885 | 0.632120558828558 |
Waiting for a call that comes every two minutes on average
A rate of 0.5 a minute: the chance that the next call comes within each wait.
EVALUATE
VAR Waits = DATATABLE ( "Minutes", DOUBLE, { { 0.5 }, { 1 }, { 2 }, { 4 } } )
RETURN
ADDCOLUMNS ( Waits, "Within", EXPON.DIST ( [Minutes], 0.5, TRUE ) )| Minutes | Within |
|---|---|
| 0.5 | 0.221199216928595 |
| 1 | 0.393469340287367 |
| 2 | 0.632120558828558 |
| 4 | 0.864664716763387 |