Computes the inverse cumulative normal distribution function values of vector elements.
Syntax
call vscdfnorminv( n, a, y )
call vmscdfnorminv( n, a, y, mode )
call vdcdfnorminv( n, a, y )
call vmdcdfnorminv( n, a, y, mode )
Include Files
- mkl_vml.f90
Input Parameters
Name |
Type |
Description |
|---|---|---|
n |
INTEGER, INTENT(IN) |
Specifies the number of elements to be calculated. |
a |
DOUBLE PRECISION for vdcdfnorminv, vmdcdfnorminv REAL, INTENT(IN) for vscdfnorminv, vmscdfnorminv DOUBLE PRECISION, INTENT(IN) for vdcdfnorminv, vmdcdfnorminv |
Array that specifies the input vector a. |
mode |
INTEGER(KIND=8), INTENT(IN) |
Overrides global VM mode setting for this function call. See vmlSetMode for possible values and their description. |
Output Parameters
Name |
Type |
Description |
|---|---|---|
y |
DOUBLE PRECISION for vdcdfnorminv, vmdcdfnorminv REAL, INTENT(OUT) for vscdfnorminv, vmscdfnorminv DOUBLE PRECISION, INTENT(OUT) for vdcdfnorminv, vmdcdfnorminv |
Array that specifies the output vector y. |
Description
The CdfNormInv function computes the inverse cumulative normal distribution function values for elements of the input vector a and writes them to the output vector y.
The inverse cumulative normal distribution function is defined as given by:
where CdfNorm(x) denotes the cumulative normal distribution function.
Useful relations:
where erfinv(x) denotes the inverse error function and erfcinv(x) denotes the inverse complementary error functions.
See also Figure "ErfInv Family Functions Relationship" in ErfInv function description for CdfNormInv function relationship with the other functions of ErfInv family.
| Argument | Result | VM Error Status | Exception |
|---|---|---|---|
| +0.5 | +0 | ||
| +1 | +∞ | VML_STATUS_SING | ZERODIVIDE |
| -0 | -∞ | VML_STATUS_SING | ZERODIVIDE |
| +0 | -∞ | VML_STATUS_SING | ZERODIVIDE |
| X < -0 | QNAN | VML_STATUS_ERRDOM | INVALID |
| X > +1 | QNAN | VML_STATUS_ERRDOM | INVALID |
| +∞ | QNAN | VML_STATUS_ERRDOM | INVALID |
| -∞ | QNAN | VML_STATUS_ERRDOM | INVALID |
| QNAN | QNAN | ||
| SNAN | QNAN | INVALID |