g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_normal_pdf (g01kac)

## 1  Purpose

nag_normal_pdf (g01kac) returns the value of the probability density function (PDF) for the Normal (Gaussian) distribution with mean $\mu$ and variance ${\sigma }^{2}$ at a point $x$.

## 2  Specification

 #include #include
 double nag_normal_pdf (double x, double xmean, double xstd, NagError *fail)

## 3  Description

The Normal distribution has probability density function (PDF)
 $fx = 1 σ ⁢ 2π e -x-μ2/2σ2 , σ>0 .$
None.

## 5  Arguments

1:     xdoubleInput
On entry: $x$, the value at which the PDF is to be evaluated.
2:     xmeandoubleInput
On entry: $\mu$, the mean of the Normal distribution.
3:     xstddoubleInput
On entry: $\sigma$, the standard deviation of the Normal distribution.
Constraint: $z<{\mathbf{xstd}}\sqrt{2\pi }<1.0/z$, where $z={\mathbf{nag_real_safe_small_number}}$, 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, ${\mathbf{xstd}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{xstd}}×\sqrt{2.0\pi }>{\mathbf{nag_real_safe_small_number}}$.
NE_UNDERFLOW
Computation abandoned owing to underflow of $\frac{1}{\left(\sigma ×\sqrt{2\pi }\right)}$.

Not applicable.

Not applicable.

None.

## 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)