Об Использовании Распределения Стьюдента В Задачах Теории Вероятностей И Математической Статистики

Bening, V. E.; Королев, Виктор Юрьевич; Korolev, Viktor Yur'evich

doi:10.4213/tvp201

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…. , X n be independent, EX i = 0 and 0 (1). Then there exists a finite positive number C 1 (γ) depending only on γ such that…”

Section: General Casementioning

confidence: 99%

“…As is known, if Λ n has the inverse gamma distribution with parameters r 2 and n 2 , then Λ −1 n has the gamma distribution with the same parameters. Therefore, we have , x ∈ R, see, e. g., [1].…”

Section: Estimates Of the Rate Of Convergence Of The Distributions Of...mentioning

confidence: 99%

“…1)/2 e −nλ/2 dλ = where γ( • , • ) and Γ( • , • ) are the lower and upper incomplete gamma-functions, respectively. So, from theorem 9 we obtain the following result.…”

mentioning

confidence: 99%

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Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions

Korolev¹,

Dorofeeva²

2015

Preprint

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Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second. These results are extended to Poisson-binomial, binomial and Poisson random sums. Under the same conditions, bounds are obtained for the accuracy of the approximation of the distributions of mixed Poisson random sums by the corresponding limit law. In particular, these bounds are constructed for the accuracy of approximation of the distributions of geometric, negative binomial and Poisson-inverse gamma (Sichel) random sums by the Laplace, variance gamma and Student distributions, respectively. All absolute constants are written out explicitly.

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“…. , X n be independent, EX i = 0 and 0 (1). Then there exists a finite positive number C 1 (γ) depending only on γ such that…”

Section: General Casementioning

confidence: 99%

Section: Estimates Of the Rate Of Convergence Of The Distributions Of...mentioning

confidence: 99%

See 1 more Smart Citation

Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions

Korolev¹,

Dorofeeva²

2015

Preprint

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Second-Order Chebyshev–Edgeworth and Cornish–Fisher Expansions for Distributions of Statistics Constructed from Samples with Random Sizes

2020

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On the approximation accuracy for quantiles in a random-size sample

Pagurova

2008

MoscowUniv.Comput.Math.Cybern.

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Об Использовании Распределения Стьюдента В Задачах Теории Вероятностей И Математической Статистики

Cited by 6 publications

References 21 publications

Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions

Bounds of the accuracy of the normal approximation to the distributions of random sums under relaxed moment conditions

Second-Order Chebyshev–Edgeworth and Cornish–Fisher Expansions for Distributions of Statistics Constructed from Samples with Random Sizes

On the approximation accuracy for quantiles in a random-size sample

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