Abstract
We present a notion of semi-self-decomposability for distributions with support in Z +. We show that discrete semi-self-decomposable distributions are infinitely divisible and are characterized by the absolute monotonicity of a specific function. The class of discrete semi-self-decomposable distributions is shown to contain the discrete semistable distributions and the discrete geometric semistable distributions. We identify a proper subclass of semi-self-decomposable distributions that arise as weak limits of subsequences of binomially thinned sums of independent Z +-valued random variables. Multiple semi-self-decomposability on Z + is also discussed.
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Bouzar, N. Semi-self-decomposable distributions on Z+ . Ann Inst Stat Math 60, 901–917 (2008). https://doi.org/10.1007/s10463-007-0124-6
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DOI: https://doi.org/10.1007/s10463-007-0124-6