is described in nag_stat_prob_landau (g01et) and nag_stat_pdf_landau (g01mt)), using either linear or quadratic interpolation or rational approximations which mimic the asymptotic behaviour. Further details can be found in Kölbig and Schorr (1984).

It can also be used to generate Landau distributed random numbers in the range

0 < x < 1

References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

Parameters

1: $x$ – double scalar: The argument $x$ of the function.

Constraint: $0.0 < x < 1.0$ .

None.

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).

Errors or warnings detected by the function:

$ifail = 1$

On entry,	$x \leq 0.0$ ,
or	$x \geq 1.0$ .

$ifail = - 99$: 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.

At least

5 - 6

significant digits are correct. Such accuracy is normally considered to be adequate for applications in large scale Monte–Carlo simulations.

None.

This example evaluates

Φ^{- 1} (x)

x = 0.5

, and prints the results.

Open in the MATLAB editor: g01ft_example

function g01ft_example


fprintf('g01ft example results\n\n');

x = 0.5;
[psix, ifail] = g01ft(x);

fprintf('Psi(%5.1f) = %7.4f\n', x, psix)

g01ft example results

Psi(  0.5) =  1.3558

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