1: $x$ – double scalar: $x$ , the value at which the PDF is to be evaluated.
2: $xmean$ – double scalar: $μ$ , the mean of the Normal distribution.
3: $xstd$ – double scalar: $σ$ , the standard deviation of the Normal distribution.

Constraint: $z < xstd \sqrt{2 π} < 1.0 / z$ , where $z = x02am ()$ , the safe range parameter.

Optional Input Parameters

None.

Output Parameters

1: $result$ – double scalar: The result of the function.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

ifail \neq 0

, then nag_stat_pdf_normal (g01ka) returns

0.0

$ifail = 1$: Constraint: $xstd \times \sqrt{2.0 π} > U$ , where $U$ is the safe range parameter as defined by nag_machine_real_safe (x02am).

$ifail = 2$: Computation abandoned owing to underflow of $\frac{1}{(σ \times \sqrt{2 π})}$ .

$ifail = 3$: Computation abandoned owing to an internal calculation overflowing.

This rarely occurs, and is the result of extreme values of the arguments x, xmean or xstd.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

None.

Example

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

Open in the MATLAB editor: g01ka_example

function g01ka_example


fprintf('g01ka example results\n\n');

x      = [1, 4, 0.1,   1];
xmean  = [0, 2, 0,     0];
xstd   = [1, 1, 0.01, 10];
result = x;
fprintf('  x             mean          standard      pdf\n');
fprintf('                              deviation\n');

for i=1:numel(x)
 [result(i), ifail] = g01ka( ...
			     x(i), xmean(i), xstd(i));
end

fprintf('%13.5e %13.5e %13.5e %13.5e\n', [x; xmean; xstd; result]);

g01ka_plot;



function g01ka_plot
 
  fig1 = figure;
  hold on;
  xmean  = [0, 0,   1];
  xstd   = [1, 0.3, 0.6];
  x{1} = [-3:0.05:3];
  x{2} = [-1.2:0.025:1.2];
  x{3} = [-1:0.05:3];
  mu = '\mu';
  sigma = '\sigma';
  for i=1:3
    for j=1:numel(x{i})
      [y{i}(j), ifail] = g01ka( ...
				x{i}(j), xmean(i), xstd(i));
    end
    plot(x{i},y{i});
    l{i} = sprintf('%s = %3.1f, %s = %3.1f', mu, xmean(i), sigma, xstd(i));
  end
  legend(l);
  xlabel('x');
  title('Gaussian Functions (or Normal Distributions)');
  hold off;

g01ka example results

  x             mean          standard      pdf
                              deviation
  1.00000e+00   0.00000e+00   1.00000e+00   2.41971e-01
  4.00000e+00   2.00000e+00   1.00000e+00   5.39910e-02
  1.00000e-01   0.00000e+00   1.00000e-02   7.69460e-21
  1.00000e+00   0.00000e+00   1.00000e+01   3.96953e-02

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox