Classical Symmetric Laplace Distribution

Samuel Kotz, Tomaz J. Kozubowski and Krzysztof Podgórski
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Samuel Kotz: George Washington University, Department of Engineering Management and Systems Engineering
Tomaz J. Kozubowski: University of Nevada, Department of Mathematics
Krzysztof Podgórski: Indiana University—Purdue University, Department of Mathematical Sciences

Chapter 2 in The Laplace Distribution and Generalizations, 2001, pp 15-131 from Springer

Abstract: Abstract In the course of our study of the Laplace distribution and its generalizations we have noticed that quite often in the statistical literature this distribution is used not on its own merits but as a source for counterexamples for other (mainly normal) distributions. It would seem that it has been created solely to provide examples of curiosity, nonregularity, and pathological behavior. In studies with probabilistic content, the distribution serves as a tool for limiting theorems and representations with the emphasis on analyzing its differences from the classical theory based on the “sound” foundations of normality. One gets the impression that the “sharp needle” at the origin of the Laplace distribution where the bulk of the density is concentrated generates a ripple effect that affects the behavior over its whole support including the tails.7. These observations prompted us to initiate a detailed study of the Laplace distribution on its own merits without constant intruding comparisons and analogues.

Keywords: Order Statistic; Maximum Likelihood Estimator; Sample Median; Laplace Distribution; Tolerance Interval (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0173-1_2

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DOI: 10.1007/978-1-4612-0173-1_2

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