In the note, we study small deviation probabilities for sums of independent, identically distributed positive random variables whose distribution function is slowly varying at zero. Bibliography: 5 titles.
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T. Höglund, “A unified formulation of the central limit theorem for small and large deviations from the mean,” Z. Wahrsch. verw. Geb., 49, 105–117 (1979).
L. V. Rozovsky, “Small deviation probabilities for a class of distributions with power decrease at zero,” Zap. Nauchn. Semin. POMI, 328, 182–190 (2005).
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L. V. Rozovsky, “Remarks on a link between the Laplace transform and distribution function of a nonnegative random variable,” Statistics and Probability Letters, 79, 1501–1508 (2009).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 412, 2013, pp. 237–251.
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Rozovsky, L.V. Small Deviation Probabilities for Sums of Independent Positive Random Variables with a Distribution that Slowly Varies at Zero. J Math Sci 204, 155–164 (2015). https://doi.org/10.1007/s10958-014-2194-3
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DOI: https://doi.org/10.1007/s10958-014-2194-3