NAG FL Interface
g01kaf (pdf_​normal)

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1 Purpose

g01kaf returns the value of the probability density function (PDF) for the Normal (Gaussian) distribution with mean μ and variance σ2 at a point x.

2 Specification

Fortran Interface
Function g01kaf ( x, xmean, xstd, ifail)
Real (Kind=nag_wp) :: g01kaf
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x, xmean, xstd
C Header Interface
#include <nag.h>
double  g01kaf_ (const double *x, const double *xmean, const double *xstd, Integer *ifail)
The routine may be called by the names g01kaf or nagf_stat_pdf_normal.

3 Description

The Normal distribution has probability density function (PDF)
f(x) = 1 σ 2π e -(x-μ)2/2σ2 ,  σ>0 .  

4 References


5 Arguments

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: μ, the mean of the Normal distribution.
3: xstd Real (Kind=nag_wp) Input
On entry: σ, the standard deviation of the Normal distribution.
Constraint: z<xstd2π<1.0/z, where z=x02amf(), the safe range parameter.
4: ifail Integer Input/Output
On entry: ifail must be set to 0, −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 −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 −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 -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
If ifail0, then g01kaf returns 0.0.
On entry, xstd=value.
Constraint: xstd×2.0π>U, where U is the safe range parameter as defined by x02amf.
Computation abandoned owing to underflow of 1(σ×2π).
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.
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.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01kaf is not threaded in any implementation.

9 Further Comments


10 Example

This example prints the value of the Normal distribution PDF at four different points x with differing xmean and xstd.

10.1 Program Text

Program Text (g01kafe.f90)

10.2 Program Data

Program Data (g01kafe.d)

10.3 Program Results

Program Results (g01kafe.r)
GnuplotProduced by GNUPLOT 4.6 patchlevel 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 −3 −2 −1 0 1 2 3 y x Example Program Plots of the Gaussian Function (or Normal Distribution). μ=0, σ=0.3 μ=0, σ=1 μ=1, σ=0.6 gnuplot_plot_1 gnuplot_plot_2 gnuplot_plot_3