NAG FL Interface
g01kaf (pdf_​normal)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{x}$ – Real (Kind=nag_wp) Input

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

2: $\mathbf{xmean}$ – Real (Kind=nag_wp) Input

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

3: $\mathbf{xstd}$ – 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: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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

$\mathbf{ifail}=1$

On entry, $\mathbf{xstd}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{xstd}\times \sqrt{2.0\pi }>U$, where $U$ is the safe range parameter as defined by x02amf.

$\mathbf{ifail}=2$

Computation abandoned owing to underflow of $\frac{1}{(\sigma \times \sqrt{2\pi })}$.

$\mathbf{ifail}=3$

Computation abandoned owing to an internal calculation overflowing.

This rarely occurs, and is the result of extreme values of the arguments x, xmean or xstd.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results