






@Manual{stabledist,
  title  = {stabledist: Stable Distribution Function. {R} package version 0.7-1},
  author = {W\"{u}rtz, Diethelm and M\"{a}chler, Martin},
  year   = {2016},
 note    = {\url{https://CRAN.R-project.org/package=stabledist}},
}



@article{Doray2009,
author = { Louis G.   Doray  and  Shu   Mei   Jiang  and  Andrew   Luong },
title = {Some Simple Method of Estimation for the Parameters of the Discrete Stable Distribution with the Probability Generating Function},
journal = {Communications in Statistics - Simulation and Computation},
volume = {38},
number = {9},
pages = {2004-2017},
year  = {2009},
publisher = {Taylor & Francis},
doi = {10.1080/03610910903202089},
}
@article{KLEBANOV20131513,
title = {Integer valued stable random variables},
journal = {Statistics \& Probability Letters},
volume = {83},
number = {6},
pages = {1513-1519},
year = {2013},
issn = {0167-7152},
doi = {https://doi.org/10.1016/j.spl.2013.02.016},
author = {Lev B. Klebanov and Lenka Slámová},
keywords = {Stable random variables, Discrete distributions},
abstract = {The aim of this paper is to define the notion of stability for random variables on Z. A definition of discrete stable distributions is introduced and we study properties of such distributions. The generating functions are given, as well as the probabilities of lattice distribution. We show how these distributions converge to classical stable distributions and thus can be considered as a discrete approximation of their absolutely continuous counterparts.},
}
@article{Slamova,
title = {APPROXIMATED MAXIMUM LIKELIHOOD ESTIMATION
OF PARAMETERS OF DISCRETE STABLE FAMILY},
journal = {Kybernetika},
volume = {50},
author = {Lenka Slámová and Lev B. Klebanov},
number = {6},
pages = {1065--1076},
year = {2014},
}





@article{soltani2009,
title = {A class of discrete distributions induced by stable laws},
journal = {Statistics \& Probability Letters},
volume = {79},
number = {14},
pages = {1608-1614},
year = {2009},
issn = {0167-7152},
doi = {https://doi.org/10.1016/j.spl.2009.03.030},
author = {A.R. Soltani and A. Shirvani and F. Alqallaf},
abstract = {A new class of discrete probability distributions with infinite second moments is introduced and studied. The class is induced by stable laws, and contains the discrete stable distributions. Members of this class appear to be suitable substitutes for the Poisson distributions, as underlying statistical distributions for certain erratic phenomena. A case study on blackhole data is provided.}
}




@article{DEVROYE1993349,
title = {A triptych of discrete distributions related to the stable law},
journal = {Statistics \& Probability Letters},
volume = {18},
number = {5},
pages = {349-351},
year = {1993},
issn = {0167-7152},
doi = {https://doi.org/10.1016/0167-7152(93)90027-G},
author = {Luc Devroye},
keywords = {Discrete stable distribution, random variate generation, distribution theory, Linnik's distribution},
abstract = {We derive useful distributional representations for three discrete laws: the discrete stable distribution of Steutel and Van Harn, the discrete Linnik distribution introduced by Pakes, and a distribution of Sibuya. These representations may be used to obtain simple uniformly fast random variate generators.}
}

@book{steutel2003infinite,
  title={Infinite Divisibility of Probability Distributions on the Real Line},
  author={Steutel, F.W. and van Harn, K.},
  isbn={9780824707248},
  lccn={03062463},
  series={Chapman \& Hall/CRC Pure and Applied Mathematics},

  year={2003},
  publisher={Taylor \& Francis}
}


@article{CHRISTOPH1998243,
title = {Discrete stable random variables},
journal = {Statistics \& Probability Letters},
volume = {37},
number = {3},
pages = {243-247},
year = {1998},
issn = {0167-7152},
doi = {https://doi.org/10.1016/S0167-7152(97)00123-5},
author = {Gerd Christoph and Karina Schreiber},
keywords = {Strictly stable and discrete stable random variables, Explicit and asymptotic formulae for probabilities, Rate of convergence},
abstract = {In Steutel and van Ham (1979) a discrete analogue of stable random variables was introduced. In the present note we consider some explicit and asymptotic formulae for the probabilities of discrete stable random variables and give rates for the convergence of sequences of certain discrete stable random variables to a stable one.}
}

@article{Steutel_1979,
author = {F. W. Steutel and K. van Harn},
title = {{Discrete Analogues of Self-Decomposability and Stability}},
volume = {7},
journal = {The Annals of Probability},
number = {5},
publisher = {Institute of Mathematical Statistics},
pages = {893 -- 899},
keywords = {discrete distribution, domain of attraction, Infinitely divisible, self-decomposable, Stable, unimodal},
year = {1979},
doi = {10.1214/aop/1176994950},
}

@article{Remillard2000,
author = {Bruno Rémillard and Radu Theodorescu},
doi = {doi:10.1524/strm.2000.18.4.349},
title = {INFERENCE BASED ON THE EMPIRICAL PROBABILITY GENERATING FUNCTION FOR MIXTURES OF {P}OISSON DISTRIBUTIONS},
journal = {Statistics \& Risk Modeling},
number = {4},
volume = {18},
year = {2000},
pages = {349--366}
}




@article{Marcheselli,
author = { M.   Marcheselli  and  A.   Baccini  and  L.   Barabesi },
title = {Parameter Estimation for the Discrete Stable Family},
journal = {Communications in Statistics - Theory and Methods},
volume = {37},
number = {6},
pages = {815-830},
year  = {2008},
publisher = {Taylor & Francis},
doi = {10.1080/03610920701570298},

URL = { 
        https://doi.org/10.1080/03610920701570298
    
},
eprint = { 
        https://doi.org/10.1080/03610920701570298
    
}

}













