# NAG CL Interfaceg01kac (pdf_​normal)

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## 1Purpose

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 $x$.

## 2Specification

 #include
 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.

## 3Description

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

None.

## 5Arguments

1: $\mathbf{x}$double Input
On entry: $x$, the value at which the PDF is to be evaluated.
2: $\mathbf{xmean}$double Input
On entry: $\mu$, the mean of the Normal distribution.
3: $\mathbf{xstd}$double Input
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: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

If ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_NOERROR, then g01kac returns $0.0$.
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
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.
NE_OVERFLOW
Computation abandoned owing to an internal calculation overflowing.
NE_REAL
On entry, ${\mathbf{xstd}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{xstd}}×\sqrt{2.0\pi }>U$, where $U$ is the safe range parameter as defined by X02AMC.
NE_UNDERFLOW
Computation abandoned owing to underflow of $\frac{1}{\left(\sigma ×\sqrt{2\pi }\right)}$.

Not applicable.

## 8Parallelism and Performance

g01kac is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01kace.c)

### 10.2Program Data

Program Data (g01kace.d)

### 10.3Program Results

Program Results (g01kace.r)