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A unified formulation of the central limit theorem for small and large deviations from the mean. (English) Zbl 0416.60030


MSC:

60F10 Large deviations
60F05 Central limit and other weak theorems
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[1] Bahadur, R. R.; Ranga Rao, R., On deviations of the sample mean, Ann. Math. Statist., 31, 1015-1027 (1960) · Zbl 0101.12603
[2] Borokov, A. A.; Rogozin, B. A., On the multi-dimensional central limit theorem, Theor. Probability Appl., 10, No. 1, 55-62 (1965)
[3] Blackwell, D.; Hodges, J. L., The probability in the extreme tail of a convolution, Ann. Math. Statist., 30, 1113-1120 (1959) · Zbl 0099.35105
[4] Feller, W., An introduction to probability theory and its applications. Vol. 1 (1950), New York: Wiley, New York · Zbl 0039.13201
[5] Feller, W., An introduction to probability theory and its applications. Vol. 2 (1950), New York: Wiley, New York · Zbl 0039.13201
[6] Cramér, H., Sur un nouveau théorème-limite de la théorie des probabilités, Actualités scientifiques et industrielles (1938), Paris: Hermann, Paris
[7] Höglund, T., A refined saddle point approximation, Ark. Mat., 12, 173-180 (1974) · Zbl 0325.60035
[8] Ibragimov, I. A.; Linnik, Yu. V., Independent and stationary sequences of random variables (1971), Groningen: Wolters-Noordhoff, Groningen · Zbl 0219.60027
[9] Petrov, V. V., On the probabilities of large deviations of sums of independent random variables, Theor. Probability Appl., 10, 287-298 (1965) · Zbl 0235.60028
[10] Petrov, V. V., Sums of independent random variables (1975), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0322.60043
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