NAG FL Interface
g01kqf (pdf_​normal_​vector)

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1 Purpose

g01kqf returns a number of values of the probability density function (PDF), or its logarithm, for the Normal (Gaussian) distributions.

2 Specification

Fortran Interface
Subroutine g01kqf ( ilog, lx, x, lxmu, xmu, lxstd, xstd, pdf, ivalid, ifail)
Integer, Intent (In) :: ilog, lx, lxmu, lxstd
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: ivalid(*)
Real (Kind=nag_wp), Intent (In) :: x(lx), xmu(lxmu), xstd(lxstd)
Real (Kind=nag_wp), Intent (Out) :: pdf(*)
C Header Interface
#include <nag.h>
void  g01kqf_ (const Integer *ilog, const Integer *lx, const double x[], const Integer *lxmu, const double xmu[], const Integer *lxstd, const double xstd[], double pdf[], Integer ivalid[], Integer *ifail)
The routine may be called by the names g01kqf or nagf_stat_pdf_normal_vector.

3 Description

The Normal distribution with mean μi, variance σi2; has probability density function (PDF)
f (xi,μi,σi) = 1 σi2π e -(xi-μi)2/2σi2 ,  σi>0 .  
The input arrays to this routine are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See Section 2.6 in the G01 Chapter Introduction for further information.

4 References

None.

5 Arguments

1: ilog Integer Input
On entry: the value of ilog determines whether the logarithmic value is returned in PDF.
ilog=0
f(xi,μi,σi), the probability density function is returned.
ilog=1
log(f(xi,μi,σi)), the logarithm of the probability density function is returned.
Constraint: ilog=0 or 1.
2: lx Integer Input
On entry: the length of the array x.
Constraint: lx>0.
3: x(lx) Real (Kind=nag_wp) array Input
On entry: xi, the values at which the PDF is to be evaluated with xi=x(j), j=((i-1) mod lx)+1, for i=1,2,,max(lx,lxstd,lxmu).
4: lxmu Integer Input
On entry: the length of the array xmu.
Constraint: lxmu>0.
5: xmu(lxmu) Real (Kind=nag_wp) array Input
On entry: μi, the means with μi=xmu(j), j=((i-1) mod lxmu)+1.
6: lxstd Integer Input
On entry: the length of the array xstd.
Constraint: lxstd>0.
7: xstd(lxstd) Real (Kind=nag_wp) array Input
On entry: σi, the standard deviations with σi=xstd(j), j=((i-1) mod lxstd)+1.
Constraint: xstd(j)0.0, for j=1,2,,lxstd.
8: pdf(*) Real (Kind=nag_wp) array Output
Note: the dimension of the array pdf must be at least max(lx,lxstd,lxmu).
On exit: f(xi,μi,σi) or log(f(xi,μi,σi)).
9: ivalid(*) Integer array Output
Note: the dimension of the array ivalid must be at least max(lx,lxstd,lxmu).
On exit: ivalid(i) indicates any errors with the input arguments, with
ivalid(i)=0
No error.
ivalid(i)=1
σi<0.
10: 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:
ifail=1
On entry, at least one value of xstd was invalid.
Check ivalid for more information.
ifail=2
On entry, ilog=value.
Constraint: ilog=0 or 1.
ifail=3
On entry, array size=value.
Constraint: lx>0.
ifail=4
On entry, array size=value.
Constraint: lxmu>0.
ifail=5
On entry, array size=value.
Constraint: lxstd>0.
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.
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.
ifail=-999
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

g01kqf is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example prints the value of the Normal distribution PDF at four different points xi with differing μi and σi.

10.1 Program Text

Program Text (g01kqfe.f90)

10.2 Program Data

Program Data (g01kqfe.d)

10.3 Program Results

Program Results (g01kqfe.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