nag_normal_pdf (g01kac) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG 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


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

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

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

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)

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 Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014