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On the Lévy Measure of the Lognormal and the LogCauchy Distributions

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  • Lennart Bondesson

    (Umeaå University)

Abstract

The densities of the Lévy measure and the Thorin measure of the standard lognormal distribution are approximated and presented in graphs. Moreover, the behavior of these densities at 0 and ∞ is studied. Laplace and saddlepoint approximations are used. The infinite divisibility of the standard logCauchy distribution is given some attention in passing.

Suggested Citation

  • Lennart Bondesson, 2002. "On the Lévy Measure of the Lognormal and the LogCauchy Distributions," Methodology and Computing in Applied Probability, Springer, vol. 4(3), pages 243-256, September.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:3:d:10.1023_a:1022533817579
    DOI: 10.1023/A:1022533817579
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    References listed on IDEAS

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    1. Steutel, F. W., 1973. "Some recent results in infinite divisibility," Stochastic Processes and their Applications, Elsevier, vol. 1(2), pages 125-143, April.
    2. Bondesson, Lennart & Kristiansen, Gundorph K. & Steutel, Fred W., 1996. "Infinite divisibility of random variables and their integer parts," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 271-278, July.
    3. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
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    Cited by:

    1. Toshiro Watanabe, 2022. "Second-Order Behaviour for Self-Decomposable Distributions with Two-Sided Regularly Varying Densities," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1343-1366, June.
    2. Toshiro Watanabe & Kouji Yamamuro, 2010. "Local Subexponentiality and Self-decomposability," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1039-1067, December.

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