Computes the inverse cumulative normal distribution function values of vector elements.
Syntax
FORTRAN:
call vscdfnorminv( n, a, y )
call vmscdfnorminv( n, a, y, mode )
call vdcdfnorminv( n, a, y )
call vmdcdfnorminv( n, a, y, mode )
C:
vsCdfNormInv( n, a, y );
vmsCdfNormInv( n, a, y, mode );
vdCdfNormInv( n, a, y );
vmdCdfNormInv( n, a, y, mode );
Input Parameters
Name |
Type |
Description |
|---|---|---|
n |
FORTRAN 77: INTEGER Fortran 90: INTEGER, INTENT(IN) C: const int |
Specifies the number of elements to be calculated. |
a |
FORTRAN 77: REAL for vscdfnorminv, vmscdfnorminv DOUBLE PRECISION for vdcdfnorminv, vmdcdfnorminv Fortran 90: REAL, INTENT(IN) for vscdfnorminv, vmscdfnorminv DOUBLE PRECISION, INTENT(IN) for vdcdfnorminv, vmdcdfnorminv C: const float* for vsCdfNormInv, vmsCdfNormInv const double* for vdCdfNormInv, vmdCdfNormInv |
FORTRAN: Array that specifies the input vector a. C: Pointer to an array that contains the input vector a. |
mode |
FORTRAN 77: INTEGER*8 Fortran 90: INTEGER(KIND=8), INTENT(IN) C: const MKL_INT64 |
Overrides global VML mode setting for this function call. See vmlSetMode for possible values and their description. |
Output Parameters
Name |
Type |
Description |
|---|---|---|
y |
FORTRAN 77: REAL for vscdfnorminv, vmscdfnorminv DOUBLE PRECISION for vdcdfnorminv, vmdcdfnorminv Fortran 90: REAL, INTENT(OUT) for vscdfnorminv, vmscdfnorminv DOUBLE PRECISION, INTENT(OUT) for vdcdfnorminv, vmdcdfnorminv C: float* for vsCdfNormInv, vmsCdfNormInv double* for vdCdfNormInv, vmdCdfNormInv |
FORTRAN: Array that specifies the output vector y. C: Pointer to an array that contains 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 | VML 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 |