NAG Library Routine Document

G01KAF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     X – REAL (KIND=nag_wp)Input

On entry: $x$, the value at which the PDF is to be evaluated.

2:     XMEAN – REAL (KIND=nag_wp)Input

On entry: $\mu$, the mean of the Normal distribution.

3:     XSTD – REAL (KIND=nag_wp)Input

On entry: $\sigma$, the standard deviation of the Normal distribution.

Constraint: $z<\mathbf{XSTD}\sqrt{2\pi }<1.0/z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

4:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

$\mathbf{XSTD}\sqrt{2.0\pi }\le z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

$\mathbf{IFAIL}=2$

$\mathbf{XSTD}\sqrt{2.0\pi }\ge 1/z$, where $z=\mathbf{X02AMF}\left(\right)$, the safe range parameter.

$\mathbf{IFAIL}=3$

An internal calculation would overflow. This rarely occurs, and is the result of extreme values of the parameters X, XMEAN or XSTD.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01kafe.f90)

9.2  Program Data

Program Data (g01kafe.d)

9.3  Program Results

Program Results (g01kafe.r)