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Advances in Ranking and Selection, Multiple Comparisons, and Reliability pp 65–79Cite as

Discriminating Between Normal and Laplace Distributions

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Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Both normal and Laplace distributions can be used to analyze symmetric data. In this chapter, we consider the logarithm of the ratio of the maximized likelihoods to discriminate between these two distributions. We obtain the asymptotic distributions of the test statistics and it is observed that they are independent of the unknown parameters. When the underlying distribution is normal, the asymptotic distribution works quite well even when the sample size is small. But when the underlying distribution is Laplace, the asymptotic distribution does not work well for small sample sizes. In this case, we propose a bias corrected asymptotic distribution which works well even for small sample sizes. Based on the asymptotic distributions, minimum sample size needed to discriminate between these two distributions is obtained for a given probability of correct selection. Monte Carlo simulations are performed to examine how the asymptotic results work for small sample sizes and two data sets are analyzed for illustrative purposes.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kanpur, India

    Debasis Kundu

Authors
  1. Debasis Kundu
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

  2. Department of Statistics, Ohio State University, 19S8 Neil Avenue Cockins Hall, Room 404, Columbus, OH, 43210-1247, USA

    H. N. Nagaraja

  3. Department of Management Science and Statistics, University of Texas at San Antonio, 6900 N. Loop 1604 W, San Antonio, TX, 78249-0632, USA

    N. Kannan

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© 2005 Birkhäuser Boston

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Kundu, D. (2005). Discriminating Between Normal and Laplace Distributions. In: Balakrishnan, N., Nagaraja, H.N., Kannan, N. (eds) Advances in Ranking and Selection, Multiple Comparisons, and Reliability. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4422-9_4

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