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On Estimation of the Values of Jumps for Discrete Distribution Functions. / Frolov, A.N.
в: Vestnik St. Petersburg University: Mathematics, Том 57, № 3, 01.09.2024, стр. 353-359.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On Estimation of the Values of Jumps for Discrete Distribution Functions
AU - Frolov, A.N.
N1 - Export Date: 21 October 2024 Адрес для корреспонденции: Frolov, A.N.; St. Petersburg State UniversityRussian Federation; эл. почта: Andrei.Frolov@pobox.spbu.ru Сведения о финансировании: Russian Science Foundation, RSF, 23-21-00078 Текст о финансировании 1: This work is supported by the Russian Science Foundation (project no. 23-21-00078).
PY - 2024/9/1
Y1 - 2024/9/1
N2 - New inequalities for the values of jumps of discrete distribution functions are obtained. The values of jumps are estimated by linear combinations of a finite number of moments of the distributions involved. The obtained inequalities can be used for statistical estimation of the ranges of values of improbable jumps when the frequencies are zero and are not interesting as estimates. The relation of the proved inequalities to the inequalities for probabilities of unions and Cauchy–Bunyakovski and Hölder’s inequalities is discussed. © Pleiades Publishing, Ltd. 2024.
AB - New inequalities for the values of jumps of discrete distribution functions are obtained. The values of jumps are estimated by linear combinations of a finite number of moments of the distributions involved. The obtained inequalities can be used for statistical estimation of the ranges of values of improbable jumps when the frequencies are zero and are not interesting as estimates. The relation of the proved inequalities to the inequalities for probabilities of unions and Cauchy–Bunyakovski and Hölder’s inequalities is discussed. © Pleiades Publishing, Ltd. 2024.
KW - Bonferroni inequalities
KW - Cauchy–Bunyakovsky inequality
KW - Hölder’s inequality
KW - probabilities of combinations of events
KW - probabilities of unions of events
KW - value of a distribution-function jump
UR - https://www.mendeley.com/catalogue/b0d90165-3c7d-3a8a-a1d5-e2ada4fc2e8d/
U2 - 10.1134/s1063454124700201
DO - 10.1134/s1063454124700201
M3 - статья
VL - 57
SP - 353
EP - 359
JO - Vestnik St. Petersburg University: Mathematics
JF - Vestnik St. Petersburg University: Mathematics
SN - 1063-4541
IS - 3
ER -
ID: 126219193