Summary
Let X1, X2,…, Xn be i.i.d. random variables with common distribution F and let al, a2,…, an be possibly degenerate random variables independent of the X’s such that ∑ | aj|α = 1 with probability one, where α is a positive constant not greater than 2. It is proved that under further conditions on the a’s there exists a symmetric stable distribution G with characteristic exponent α such that F is close to G whenever the distribution of the linear statistic ∑ ajXj is close to F.
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© 1981 D. Reidel Publishing Company
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Shimizu, R., Davies, L. (1981). On the Stability of Characterizations of Non-Normal Stable Distributions. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8549-0_41
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DOI: https://doi.org/10.1007/978-94-009-8549-0_41
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