nag_normal_pdf (g01kac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_normal_pdf (g01kac)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_normal_pdf (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>
#include <nagg01.h>
double  nag_normal_pdf (double x, double xmean, double xstd, NagError *fail)

3  Description

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

4  References

None.

5  Arguments

1:     xdoubleInput
On entry: x, the value at which the PDF is to be evaluated.
2:     xmeandoubleInput
On entry: μ, the mean of the Normal distribution.
3:     xstddoubleInput
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:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_INTERNAL_ERROR
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.
NE_OVERFLOW
Computation abandoned owing to an internal calculation overflowing.
NE_REAL
On entry, xstd=value.
Constraint: xstd×2.0π>nag_real_safe_small_number.
NE_UNDERFLOW
Computation abandoned owing to underflow of 1σ×2π.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

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

9.1  Program Text

Program Text (g01kace.c)

9.2  Program Data

Program Data (g01kace.d)

9.3  Program Results

Program Results (g01kace.r)

Produced by GNUPLOT 4.4 patchlevel 0 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). m=0, s=0.3 m=0, s=1 m=1, s=0.6

nag_normal_pdf (g01kac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012