Asymptotic Methods in Probability and Statistics with Applications

Part of the series Statistics for Industry and Technology pp 3-17

Positive Linnik and Discrete Linnik Distributions

  • Gerd ChristophAffiliated withOtto-von-Guericke-Universität Magdeburg
  • , Karina SchreiberAffiliated withOtto-von-Guericke-Universität Magdeburg

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In this chapter, (continuous) positive Linnik and (nonnegative integer valued) discrete Linnik random variables are discussed. Rates of convergence and first terms of both the Edgeworth expansions and the expansions in the exponent of the distribution functions of certain sums of such random variables with nonnegative strictly stable as well as discrete stable limit laws are considered.

Keywords and phrases

Positive Linnik and discrete Linnik distributions discrete self-decomposability discrete stability rates of convergence Edgeworth expansions expansions in the exponent with discrete stable limit law