On Some Characterizations of the Levy Distribution

Mohammad Ahsanullah 1  and V. B. Nevzorov 2
  • 1 Rider University, New Jersey, Lawrenceville, USA
  • 2 Sankt Peterburg State University, Sankt Petersburg, Russia
Mohammad Ahsanullah and V. B. Nevzorov

Abstract

If the distribution of the linear combination of two independent and identically distributed random variables from a distribution belongs to the same distribution, then we call that distribution a stable distribution. The Levy distribution is a member of the family of stable distributions. In this paper, we will present some basic distributional properties and characterizations of the Levy distribution.

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    V. M. Zolotarev, One Dimensional Stable Distributions, Math. Monogr. 65, American Mathematical Society, Providence, 1986.

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