Geodesic
Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramér condition
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 78-103 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper studies the asymptotic behavior of a density of a sum of independent identically distributed random variables with a common absolutely continuous distribution satisfying the right-hand Cramér condition. We prove that for a definite class of such distributions the well-known asymptotic representations in local and integral limit theorems are valid in the case of large deviations of arbitrarily high order.
Keywords: independent random variables, density function, large deviations
Mots-clés : Cramér condition. 
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L. V. Rozovskii. Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramér condition. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 78-103. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a4/

[1] Borovkov A. A., Rogozin B. A., “O tsentralnoi predelnoi teoreme v mnogomernom sluchae”, Teoriya veroyatn. i ee primen., 10:1 (1965), 61–69 | MR | Zbl

[2] Daniels H. E., “Saddlepoint approximations in statistics”, Ann. Math. Statist., 25:4 (1954), 631–650 | DOI | MR | Zbl

[3] Petrov V. V., “O veroyatnostyakh bolshikh uklonenii summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 10:2 (1965), 310–322 | MR | Zbl

[4] Nagaev A. V., “Bolshie ukloneniya dlya odnogo klassa raspredelenii”, Predelnye teoremy teorii veroyatnostei, AN UzSSR, Tashkent, 1963, 56–68

[5] Kramer G., “Ob odnoi novoi predelnoi teoreme teorii veroyatnostei”, Uspekhi matem. nauk, 1944, no. 10, 166–178

[6] Bahadur R. R., Ranga Rao R., “On deviations of the sample mean”, Ann. Math. Statist., 31:4 (1960), 1015–1027 | DOI | MR | Zbl

[7] Höglund T., “A unified formulation of the central limit theorem for small and large deviations from the mean”, Z. Wahrscheinlichkeitstheor. verw. Geb., 49 (1979), 105–117 | DOI | MR | Zbl

[8] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, M., 1984, 527 pp.

[9] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972, 416 pp. | MR

[10] Statulyavichus V. A., “Predelnye teoremy dlya plotnostei i asimptoticheskie razlozheniya dlya raspredelenii summ nezavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primen., 10:4 (1965), 645–659

[11] Rozovskii L. V., “Otsenka integrala ot modulya kharakteristicheskoi funktsii obobschennogo puassonovskogo raspredeleniya po intervalu maloi dliny”, Zap. nauchn. semin. POMI, 260, 1999, 240–249 | MR

[12] Khastings N., Pikok Dzh., Spravochnik po statisticheskim raspredeleniyam, Statistika, M., 1980, 95 pp.

[13] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Fizmatgiz, M., 1962, 808 pp.

[14] Nagaev A. V., “Bolshie ukloneniya dlya odnogo klassa polozhitelnykh sluchainykh velichin”, Izv. AN UzSSR, 1963, no. 1, 18–20 | MR | Zbl

[15] Nagaev A. V., Khodzhabagyan S. S., “Predelnye teoremy, uchityvayuschie bolshie ukloneniya, dlya summ polozhitelnykh sluchainykh velichin”, Litov. matem. sb., 14:1 (1974), 149–163 | MR | Zbl

[16] Nagaev A. V., “Bolshie ukloneniya dlya summ reshetchatykh sluchainykh velichin pri vypolnenii usloviya Kramera”, Diskretn. matem., 10:3 (1998), 115–130 | MR | Zbl