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A note on the ratio of normal and Laplace random variables

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Abstract

The normal and Laplace are the two earliest known continuous distributions in statistics and the two most popular models for analyzing symmetric data. In this note, the exact distribution of the ratio | X / Y | is derived when X and Y are respectively normal and Laplace random variables distributed independently of each other. A MAPLE program is provided for computing the associated percentage points. An application of the derived distribution is provided to a discriminant problem.

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Authors and Affiliations

  1. Department of Statistics, University of Nebraska, Lincoln, NE, 68583, USA

    Saralees Nadarajah

  2. Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC, 20052, USA

    Samuel Kotz

Authors
  1. Saralees Nadarajah
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  2. Samuel Kotz
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Correspondence to Samuel Kotz.

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Nadarajah, S., Kotz, S. A note on the ratio of normal and Laplace random variables. Stat. Meth. & Appl. 15, 151–158 (2006). https://doi.org/10.1007/s10260-006-0007-7

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  • DOI: https://doi.org/10.1007/s10260-006-0007-7

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