G110: Landau Distribution

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 30.08.1985
Language: Fortran	Revised: 15.03.1993

The LANDAU function subprogram package contains six independent subprograms for the calculation of the following functions related to the Landau distribution:

The function can be used to generate Landau random numbers (see Usage).

Structure:

FUNCTION subprograms
User Entry Names: DENLAN, DISLAN, DIFLAN, XM1LAN, XM2LAN, RANLAN
Obsolete User Entry Names: DSTLAN DISLAN

Usage:

In any arithmetic expression,

DENLAN(X) has the value

DISLAN(X) has the value

DIFLAN(X) has the value

XM1LAN(X) has the value

XM2LAN(X) has the value

RANLAN(X) has the value

where DENLAN, DISLAN, DIFLAN, XM1LAN, XM2LAN, RANLAN and X are of type REAL.

To generate a set of Landau random numbers, RANLAN should be referenced repeatedly, using as argument a random number from a uniform distribution over the interval (0,1).

Method:

Approximation by rational functions. For reason of speed, RANLAN proceeds mainly by table look-up and quadratic interpolation.

Accuracy:

At least six significant digits (five for RANLAN) are correct.

Restrictions:

1. Underflow may occur for DENLAN, DISLAN and DIFLAN if X is negative and (moderately) large.
2. No test is made whether X for RANLAN lies outside the interval (0,1), and hence no error message is printed.

Notes:

This program package is a version of the CPC Program Library package LANDAU (Ref. 1).

References:

1. K.S. Kölbig and B. Schorr, A program package for the Landau distribution, Computer Phys. Comm. 31 (1984) 97-111.