Abstract
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.
I belong to the last generation of students learning the basic knowledge of statistics by Yuri Vladimirovitsch Linnik. Only a few weeks before he died I took my examination in Statistics. I remember this examination because Prof. Linnik welcomed me in German and he asked me (in German) about properties of “Maximum—LikelihoodSchätzungen.” Never before I had heard these German terms. I was prepared to answer as usually in Russian. So I learned from Prof. Linnik not only to like statistics but also during the examination that likelihoodis an old English word for probability which is used in German statistical terms too. Gerd Christoph
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Christoph, G., Schreiber, K. (2001). Positive Linnik and Discrete Linnik Distributions. In: Balakrishnan, N., Ibragimov, I.A., Nevzorov, V.B. (eds) Asymptotic Methods in Probability and Statistics with Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0209-7_1
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