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On probabilities of large deviations

Published online by Cambridge University Press:  17 April 2009

Vijay K. Rohatgi
Vijay K. Rohatgi
Affiliation:
The Catholic University of America, Washington, DC, USA.
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Abstract

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Let {Xn} be a sequence of independent identically distributed random variables and let The rate of convergence of probabilities , where 2 > r > 1, is studied.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 2 , October 1970 , pp. 277 - 285
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Davis, James Avery, “Convergence rates for probabilities of moderate deviations”, Ann. Math. Statist. 39 (1968), 2016–2028.CrossRefGoogle Scholar
[2]Erdös, P., “On a theorem of Hsu and Robbins”, Ann. Math. Statist. 20 (1949), 286–291.CrossRefGoogle Scholar
[3]Gnedenko, B.V. and Kolmogorov, A.N., Limit distributions for sums of independent random variables (Translated and annotated by Chung, K.L. with an appendix by J.L. Doob. Addison-Wesley, Cambridge, Massachussetts; 1954).Google Scholar
[4]Loève, Michel, Probability theory, 3rd ed. (Van Nostrand, Princeton, New Jersey; Toronto, Ontario; London; 1963).Google Scholar
[5]Rohatgi, V.K., “On the rate of convergence of probabilities of moderate deviation's”, J. Austral. Math. Soc. 11 (1970), 91–94.CrossRefGoogle Scholar
[6]Rubin, Herman and Sethuraman, J., “Probabilities of moderate deviations”, Sankhyā Ser. A 27 (1965), 325–346.Google Scholar
[7]Sethuraman, J., Probabilities of deviations (Indian Statistical Institute Report no. 5, 1966).Google Scholar