Probability inequalities related to Markov's theorem

被引：46

作者：

Ghosh, BK ^{[1
]}

机构：

[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA

来源：

AMERICAN STATISTICIAN | 2002年 / 56卷 / 03期

关键词：

bounds for probabilities; Berry-Esseen's; Cantelli's; Chebyshev's; Feller's; Markov's; Paley-Zygmund's and Selberg's inequalities;

D O I：

10.1198/000313002119

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A recurrent theme of interest in probability and statistics is to determine the best bounds for two probabilities, Pr(X greater than or equal to r) and Pr(s < X - mu < t), when only the mean It and the standard deviation sigma of a random variable X are known. This article addresses the issue under two circumstances, when X is arbitrary and when X is nonnegative. The answers are provided in a unified manner using only Markov's theorem. The existing literature on related inequalities is reviewed. Some examples are given to illustrate the use of the inequalities.

引用

页码：186 / 190

页数：5

共 15 条

[1]

[Anonymous], 1913, ISCHISLENIE VEROIATN

[2]

Bienayme I.-J., 1853, Comptes Rendus de l'Academie des Sciences, V37, P309

[3]

Cantelli F.P., 1929, ATTI CONGRESSO INTER, V6, P47

[4]

Chebyshev PL., 1867, J MATH PURE APPL, V12, P177

[5]

CHEBYSHEV PL, 1874, LIOUVILLES J MATH PU, V19, P157

[6]

Chung KL., 1974, COURSE PROBABILITY T

[7]

Cramer H., 1946, Mathematical Methods of Statistics

[8]

FELLER W, 1971, INTRO PERSONALITY TH, V2

[9] ON GENERALIZATIONS OF TCHEBYCHEFS INEQUALITY [J].

GODWIN, HJ .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1955, 50 (271) :923-945

[10]

Paley REAC, 1932, P CAMB PHILOS SOC, V28, P266

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