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Truncated stable random variables: characterization and simulation

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Abstract

Kanter (Ann Probab 3(4):697–707, 1975) and Chambers et al. (J Am Stat Assoc 71(354):340–344, 1976) developed a method for characterizing and simulating stable random variables, X, using nonlinear transformations involving two independent uniform random variables. Their method is scrutinized to provide a characterization and then develop a method for simulating random variables with distribution P(X ≤ x| X  > a), called here truncated stable random variables. Our characterization is rigorous when the characteristic exponent α ≠ 1. We extend our method to the case that α → 1.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Faculty of Sciences, Kuwait University, P.O. Box 5969, 13060, Safat, State of Kuwait

    A. R. Soltani

  2. Department of Statistics, College of Science, Shiraz University, 71454, Shiraz, Iran

    A. R. Soltani & A. Shirvani

Authors
  1. A. R. Soltani
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  2. A. Shirvani
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Correspondence to A. R. Soltani.

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Soltani, A.R., Shirvani, A. Truncated stable random variables: characterization and simulation. Comput Stat 25, 155–161 (2010). https://doi.org/10.1007/s00180-009-0167-7

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  • DOI: https://doi.org/10.1007/s00180-009-0167-7

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