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A characterization of the normal law

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Summary

IfX, Y, Z are three random observations from a normal population with mean zero then the characteristic function of (X/Z, Y/Z) is exp\(( - \sqrt {t^2 + u^2 } )\). It is shown in this paper that this property characterizes the normal law.

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References

  1. R. G. Laha, “On a class of distribution functions where the quotient follows the Cauchy law,”Trans. Amer. Math. Soc., 93 (1959), 205–215.

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  2. R. P. Pakshirajan and M. Sudhakara Rao, “On the generalized law of Cauchy and Gauss,”Mysore University Journal, 1967.

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Authors and Affiliations

  1. University of Mysore, India

    R. P. Pakshirajan & N. R. Mohan

Authors
  1. R. P. Pakshirajan
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  2. N. R. Mohan
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Pakshirajan, R.P., Mohan, N.R. A characterization of the normal law. Ann Inst Stat Math 21, 529–532 (1969). https://doi.org/10.1007/BF02532276

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  • DOI: https://doi.org/10.1007/BF02532276

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