is described in nag_prob_landau (g01etc) and nag_prob_density_landau (g01mtc)), 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

4

References

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

5

Arguments

1: $x$ – doubleInput: On entry: the argument $x$ of the function.

Constraint: $0.0 < x < 1.0$ .
2: $fail$ – NagError *Input/Output: The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_REAL: On entry, $x = 〈value〉$ .
Constraint: $x < 1.0$ .

On entry, $x = 〈value〉$ .
Constraint: $x > 0.0$ .

At least

5 - 6

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

nag_deviates_landau (g01ftc) is not threaded in any implementation.

None.

This example evaluates

Φ^{- 1} (x)

x = 0.5

, and prints the results.