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On the Linear Combination of Laplace and Logistic Random Variables

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  • Saralees Nadarajah
  • Samuel Kotz

Abstract

The distribution of linear combinations of random variables arises explicitly in many areas of engineering. This has increased the need to have available the widest possible range of statistical results on linear combinations of random variables. In this note, the exact distribution of the linear combination α X+β Y is derived when X and Y are Laplace and logistic random variables distributed independently of each other. Extensive tabulations of the associated percentage points obtained by inverting the derived distribution are also given.

Suggested Citation

  • Saralees Nadarajah & Samuel Kotz, 2007. "On the Linear Combination of Laplace and Logistic Random Variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(2), pages 185-194.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:2:p:185-194
    DOI: 10.1080/02664760600995072
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    References listed on IDEAS

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    1. Peter W. Glynn & Donald L. Iglehart, 1989. "The optimal linear combination of control variates in the presence of asymptotically negligible bias," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(5), pages 683-692, October.
    2. R. W. Farebrother, 1984. "The Distribution of a Positive Linear Combination of X2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(3), pages 332-339, November.
    3. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
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