DENSITY OpenBI
A distribution's density curve as a table: a Gaussian kernel, as R's density.
Group: Statistics. OpenBI’s own: DAX has no function of this name.
Syntax
DENSITY ( <table>, <value> [, <points>] [, <bandwidth>] )| Parameter | Type | Description |
|---|---|---|
table | Table | The rows whose values make the curve. |
value | Expression evaluated for each row | The number worked out for each row. |
points | Whole number optional | How many points of the curve to return, 2 to 100,000; 512 when left out. |
bandwidth | Number optional | The width of each value's bell, in the value's units. Left out or 0, it is chosen from the values. |
Returns
Table. A row a point: Value and Density, evenly spaced from three bandwidths below the smallest value to three above the largest.
Remarks
- Each value adds a small normal bell centred on itself, as wide as the bandwidth; the curve is the mean of the bells, so its area is 1.
- The bandwidth chosen by default is R's bw.nrd0: 0.9 × the smaller of the standard deviation and IQR / 1.34, × n^(−1/5).
- The densities are the exact sums of the bells. R's density() works on a binned grid, so its figures can differ a little in the later digits.
- A larger bandwidth makes a smoother curve; a smaller one follows the values more closely. Blank results are left out.
Compared with DAX
An OpenBI function: DAX has none like it, so a measure or query that uses it works in OpenBI only, not in Power BI or Analysis Services.
Examples
Seven points of the curve of delivery times
The late delivery at 45 minutes makes a second, smaller bump.
EVALUATE
VAR Times =
DATATABLE (
"Minutes", INTEGER,
{ { 12 }, { 14 }, { 15 }, { 15 }, { 16 }, { 18 }, { 19 }, { 21 }, { 22 }, { 45 } }
)
RETURN
DENSITY ( Times, [Minutes], 7 )| Value | Density |
|---|---|
| 5.00767420482771 | 0.000203923977017766 |
| 12.8384494698851 | 0.0622893752507435 |
| 20.6692247349426 | 0.0579962865514964 |
| 28.5 | 0.000451943384753828 |
| 36.3307752650574 | 1.69556701000497e-05 |
| 44.1615505301149 | 0.0160438872625909 |
| 51.9923257951723 | 0.000190144819124327 |
A bandwidth of your own
EVALUATE
VAR Times =
DATATABLE (
"Minutes", INTEGER,
{ { 12 }, { 14 }, { 15 }, { 15 }, { 16 }, { 18 }, { 19 }, { 21 }, { 22 }, { 45 } }
)
RETURN
DENSITY ( Times, [Minutes], 5, 2 )| Value | Density |
|---|---|
| 6 | 0.000229956959125922 |
| 17.25 | 0.0803822489367055 |
| 28.5 | 0.000119354375574755 |
| 39.75 | 0.000636209079841572 |
| 51 | 0.0002215924205969 |
Crates per place, in nine points
EVALUATE
DENSITY ( Places, Places[Crates], 9 )| Value | Density |
|---|---|
| -5.78635365390297 | 0.000143608850927434 |
| -2.08976524042723 | 0.00718806578648315 |
| 1.60682317304851 | 0.00946821650397828 |
| 5.30341158652426 | 0.0196265570626128 |
| 9 | 0.0850985711995334 |
| 12.6965884134757 | 0.0906419793599923 |
| 16.3931768269515 | 0.0487974948330588 |
| 20.0897652404272 | 0.00914679595881913 |
| 23.786353653903 | 0.000147819267907715 |