The exact probability distribution governing the length of a random walk of equal steps.

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Methods: Statistical

Scientific paper

The probability distribution of the length of a random walk of n equal steps in two dimensions arises in many astronomical problems. While the exact solution of this problem is known it is seldom used, perhaps because it is difficult to evaluate and seems never to have been tabulated. An approximation based on the application of the central limit theorem is used instead, which is easy to evaluate but necessarily leaves uncertainty both about the accuracy of any statistical test and about the reliability of any conclusions drawn. Such difficulties may be avoided by using the exact solution, which is evaluated here with an accuracy of typically 1 part in 10^6^. The results are presented as tables of the cumulative distribution and of the percentage points, for n in the range from 2 to 100 steps.

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