Inequalities and limit theorems for random allocations

Fazekas, István; Chuprunov, A. N.; Túri, József

doi:10.2478/v10062-011-0006-5

Cited by 2 publications

(2 citation statements)

References 10 publications

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“…Also in the same, Gordon et al (1986), accompanying distributions were obtained for the length of the longest T -contaminated head run. Fazekas and Suja (2021) shown that the accompanying distribution initially obtained by Gordon et al (1986) could as well be arrived at using the approach given by Földes (1979). After some probabilistic calculations and algebraic manipulations of the approximation of the length of the longest T -contaminated run and using the main lemma in Csáki et al (1987), more precise and accurate convergence rate was obtained for the accompanying distribution of the longest T -contaminated head run by Fazekas et al (2023) for T = 1 and T = 2.…”

Section: Introductionmentioning

confidence: 92%

Report of the International Conference on Generalized Functions (Debrecen, Hungary, 1984)

Fazekas¹,

Gesztelyi²,

Száz³

2022

Publ. Math. Debrecen

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Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and rank classification techniques based on performance metrics such as accuracy, sensitivity, and specificity. However, reported performance scores may not always serve as a reliable basis for research ranking. This can be attributed to undisclosed or unconventional practices related to cross-validation, typographical errors, and other factors. In a given experimental setup, with a specific number of positive and negative test items, most performance scores can assume specific, interrelated values. In this paper, we introduce numerical techniques to assess the consistency of reported performance scores and the assumed experimental setup. Importantly, the proposed approach does not rely on statistical inference but uses numerical methods to identify inconsistencies with certainty. Through three different applications related to medicine, we demonstrate how the proposed techniques can effectively detect inconsistencies, thereby safeguarding the integrity of research fields. To benefit the scientific community, we have made the consistency tests available in an open-source Python package.

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Section: Introductionmentioning

confidence: 92%

Report of the International Conference on Generalized Functions (Debrecen, Hungary, 1984)

Fazekas¹,

Gesztelyi²,

Száz³

2022

Publ. Math. Debrecen

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“…Also in [6], accompanying distributions were obtained for the length of the longest T -contaminated head run. In [4], it was shown that the accompanying distributions of [6] can be obtained by the method of Földes [5].…”

Section: Introductionmentioning

confidence: 99%

Convergence rate for the longest T-contaminated runs of heads. Paper with detailed proofs

Fazekas¹,

Fazekas²,

Suja³

2023

Preprint

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We study the length of T -contaminated runs of heads in the well-known coin tossing experiment. A T -contaminated run of heads is a sequence of consecutive heads interrupted by T tails. For T = 1 and T = 2 we find the asymptotic distribution for the first hitting time of the T contaminated run of heads having length m; furthermore, we obtain a limit theorem for the length of the longest T -contaminated head run. We prove that the rate of the approximation of our accompanying distribution for the length of the longest T -contaminated head run is considerably better than the previous ones. For the proof we use a powerful lemma by Csáki, Földes and Komlós, see [1].

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Inequalities and limit theorems for random allocations

Cited by 2 publications

References 10 publications

Report of the International Conference on Generalized Functions (Debrecen, Hungary, 1984)

Report of the International Conference on Generalized Functions (Debrecen, Hungary, 1984)

Convergence rate for the longest T-contaminated runs of heads. Paper with detailed proofs

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