Toward a usable theory of Cherno Bounds for heterogeneous and partially dependent random variables
نویسنده
چکیده
Let X be a sum of real valued random variables and have a bounded mean EEX]. The generic Chernoo-Hoeeding estimate for large deviations of X is: PrfX?EEX] ag min 0 e ?(a+EEX]) EEe X ], which applies with a 0 to random variables with very small tails. At issue is how to use this method to attain sharp and useful estimates. We present a number of Chernoo-Hoeeding bounds for sums of random variables that may have a variety of dependent relationships and that may be heterogeneously distributed. 1 Summary In the analysis of probabilistic algorithms, some of the following problems may arise, possibly in complex combinations.
منابع مشابه
Some Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.
متن کاملOn the bounds in Poisson approximation for independent geometric distributed random variables
The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method. Some results related to random sums of independent geometric distributed random variables are also investigated.
متن کاملBounds for CDFs of Order Statistics Arising from INID Random Variables
In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a main concern for researchers. A cumulative distribution function (CDF) of these random variables (Fi:n) is a complex manipulating, long time consuming and a software-intensive tool that takes more and more times. Therefore, obtaining approximations a...
متن کاملSampling of Multiple Variables Based on Partially Ordered Set Theory
We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation...
متن کاملAcceptable random variables in non-commutative probability spaces
Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.
متن کامل