The Von Mises and Fisher Directional Distributions

TOMS571 is a FORTRAN77 library which implements ACM TOMS algorithm 571, containing routines to determine the concentration parameter from the average modulus of a set of sample vectors, and vice versa, for both the von Mises (circular) and Fisher (spherical) distributions of directions.

The text of many ACM TOMS algorithms is available online through ACM: or NETLIB:


TOMS571 is available in a FORTRAN77 version.

Related Data and Programs:

PROB, a FORTRAN90 library which contains routines to sample the von Mises and Fisher distributions.


  1. Geoffrey Hill,
    Algorithm 571, Statistics for von Mises's and Fisher's Distributions of Directions, I1(x)/I0(x), I1.5(x)/I0.5(x), and Their Inverses,
    ACM Transactions on Mathematical Software,
    Volume 7, Number 2, June 1981, pages 233-238.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 07 January 2007.