On asymptotic expansions of probability functions

Bergström, Harald

doi:10.1080/03461238.1951.10432122

Cited by 33 publications

(16 citation statements)

References 2 publications

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“…Comparing (3.3) with (2.6) (s = 2) we see that in (3.3) there is no exponential factor. Note that (3.3) is not the classical version of Bergstr6m's expansion as in [3,4,18]. In fact, analogous expansion was used by Deheuvels and Pfeifer in [9].…”

Section: Asymptotic Expansion In Le Cam's Theoremmentioning

confidence: 86%

Approximation of the generalized Poisson binomial distribution: Asymptotic expansions

Čekanavičius¹

1997

Lith Math J

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Section: Asymptotic Expansion In Le Cam's Theoremmentioning

confidence: 86%

Approximation of the generalized Poisson binomial distribution: Asymptotic expansions

Čekanavičius¹

1997

Lith Math J

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“…From the Bergstr6m identity [4] we obtain that the left-hand side of (2.10) is less than or equal to H -~FI = At + A2+A4.…”

Section: Iif-gll F Lp(t)--(t)lzdt Ip'(t)-and(t)l'dtmentioning

confidence: 97%

Remarks on estimates in the total-variation metric

Čekanavičius

2000

Lith Math J

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Abstract. For sums of independent lattice random variables, the limiting normal approximation is trivial if the total-variation distance is considered. In this paper, we show that the normal distribution can be replaced by a suitably chosen lattice distribution. Mixtures of distributions are approximated by a convolution of the normal and Poisson laws. Construction of an asymptotic expansion is discussed.

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“…The proofs are based on the application of the Taylor's formula, properties of the limiting Gaussian distribution, induction in n and iterations of the estimates. Methods of such kind were developed earlier for the estimation of the convergence speed in the Central Limit Theorem (Bergstrom 1951;Kuelbs and Kurtz 1974;Butzer et al 1975;Paulauskas 1976;Zolotarev 1976;Sazonov 1981;Bolthausen 1982;Bentkus and Ra6kauskas 1982a, b;Haeusler 1984;G6tze 1986;etc.). Our proofs differ from that usually used to obtain limit theorems for probabilities of large deviations (Ibragimov and Linnik 1965;Petrov 1975;Rudzkis et al 1979; etc.)…”

Section: Corollary 12 For Every Function F: R ~ ~ R T Such That Limmentioning

confidence: 98%