NAG CL Interface
g01kac (pdf_​normal)

1 Purpose

g01kac 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

#include <nag.h>
double  g01kac (double x, double xmean, double xstd, NagError *fail)
The function may be called by the names: g01kac, nag_stat_pdf_normal or nag_normal_pdf.

3 Description

The Normal distribution has probability density function (PDF)
fx = 1 σ 2π e -x-μ2/2σ2 ,  σ>0 .  

4 References


5 Arguments

1: x double Input
On entry: x, the value at which the PDF is to be evaluated.
2: xmean double Input
On entry: μ, the mean of the Normal distribution.
3: xstd double Input
On entry: σ, the standard deviation of the Normal distribution.
Constraint: z<xstd2π<1.0/z, where z=nag_real_safe_small_number, the safe range parameter.
4: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
Computation abandoned owing to an internal calculation overflowing.
On entry, xstd=value.
Constraint: xstd×2.0π>U, where U is the safe range parameter as defined by X02AMC.
Computation abandoned owing to underflow of 1σ×2π.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g01kac 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 (g01kace.c)

10.2 Program Data

Program Data (g01kace.d)

10.3 Program Results

Program Results (g01kace.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