Probability Inequalities Related to Markov's Theorem

Autor:	B. K. Ghosh
Rok vydání:	2002
Předmět:	Statistics and Probability Combinatorics Probability theory Markov chain Chebyshev's inequality General Mathematics Probability distribution Probability and statistics Statistics Probability and Uncertainty Markov model Random variable Standard deviation Mathematics
Zdroj:	The American Statistician. 56:186-190
ISSN:	1537-2731 0003-1305
DOI:	10.1198/000313002119
Popis:	A recurrent theme of interest in probability and statistics is to determine the best bounds for two probabilities, Pr(X ≥ r) and Pr(s < X - μ < t), when only the mean μ and the standard deviation σ 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7a017d2b35313c2d4599efb0a70c47c3 https://doi.org/10.1198/000313002119 Zobrazit plný text záznamu