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The bivariate gamma distribution and the random walk problem

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Summary

The relation between the random walk problem in one dimension and the joint distribution of two correlated gamma variates of parameter ½ is firstly established. It is shown that the two variates which represent respectively the squares of distances from the origin (properly normalised) after P steps and P+Q (=N) steps in one dimension are a pair of correlated gamma variates with parameter ½. This is used as a heuristic principle to set up similar bivariate gamma distribution with parameters 1 by examining the corresponding problem of random walk in two dimensions. Finally, the results are extended to the case of generaln-dimensional random walk where it is shown to lead to the bivariate gamma distribution with parametern/2.

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Authors and Affiliations

  1. Centre of Advanced Study in Physics, University of Madras, Madras-25, India

    R. Srinvasan

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  1. R. Srinvasan
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Communicated by Dr. G. N. Ramachandran,f.a.sc.

Contribution No. 172 from the Centre of Advanced Study in Physics, University of Madras.

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Srinvasan, R. The bivariate gamma distribution and the random walk problem. Proc. Indian Acad. Sci. 62, 358–366 (1965). https://doi.org/10.1007/BF03046529

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  • DOI: https://doi.org/10.1007/BF03046529

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