POISSON.DIST
The Poisson distribution of a mean at a number of events, as a probability or a cumulative one.
Group: Statistics. Compatible with DAX.
Syntax
POISSON.DIST ( <x>, <mean>, <cumulative> )| Parameter | Type | Description |
|---|---|---|
x | Whole number | The number of events, 0 or more; rounded to a whole number. |
mean | Number | How many events are expected, 0 or more. |
cumulative | Boolean | TRUE for the chance of at most x events; FALSE for exactly x. |
Returns
Number. The probability of exactly x events, or of x or fewer.
Remarks
- An x that is not whole is rounded to the nearest whole number: 2.5 counts as 3.
- With a mean of 0, no events is certain: the probability of 0 events is 1.
- A negative x or mean is an error.
Examples
Exactly three, or at most three
EVALUATE
ROW (
"Exactly 3", POISSON.DIST ( 3, 2.5, FALSE ),
"At most 3", POISSON.DIST ( 3, 2.5, TRUE )
)| Exactly 3 | At most 3 |
|---|---|
| 0.213763017249736 | 0.757576133133066 |
Complaints a week, at 1.6 on average
EVALUATE
VAR Counts = DATATABLE ( "Complaints", INTEGER, { { 0 }, { 1 }, { 2 }, { 3 }, { 4 } } )
RETURN
ADDCOLUMNS (
Counts,
"Exactly", POISSON.DIST ( [Complaints], 1.6, FALSE ),
"At most", POISSON.DIST ( [Complaints], 1.6, TRUE )
)| Complaints | Exactly | At most |
|---|---|---|
| 0 | 0.201896517994655 | 0.201896517994655 |
| 1 | 0.323034428791449 | 0.524930946786104 |
| 2 | 0.258427543033159 | 0.783358489819263 |
| 3 | 0.137828022951018 | 0.921186512770281 |
| 4 | 0.0551312091804073 | 0.976317721950688 |