A Convergence Theorem for the Standard Luria–Delbrück Distribution

نویسنده

  • M. Möhle
چکیده

A new scaling for the standard discrete Luria-Delbrück distribution is provided which leads to a weak convergence result as the parameter of the distribution tends to infinity. We show that the stable limiting probability measure has the Fourier transform t → exp(−π|t|/2−it log |t|). For the corresponding density an integral representation is derived, which differs from that found in a closely related paper of Kepler and Oprea [4]. In addition, we indicate how the approach is connected to more general compound Poisson distributions.

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تاریخ انتشار 2003