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PROBABILITY INEQUALITIES FOR SUMS OF BOUNDED RANDOM VARIABLES
, 1962
"... Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges of the s ..."
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Cited by 2217 (2 self)
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Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr(SES> nt) depend only on the endpoints of the ranges
On a test of whether one of two random variables is stochasitcally larger than the other
 ANNALS OF MATHEMATICAL STATISTICS
, 1947
"... ..."
Random Variables
"... on Function The cumulative distribution function F X (x) for a random variable X(.), or when convenient represented by just X,is defined for all x as follows F X (x)=Pr{.:X(.)#x}Pr{X#x} It is sufficient information to calculate the probabilities of all allowable events and as a result is called a t ..."
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on Function The cumulative distribution function F X (x) for a random variable X(.), or when convenient represented by just X,is defined for all x as follows F X (x)=Pr{.:X(.)#x}Pr{X#x} It is sufficient information to calculate the probabilities of all allowable events and as a result is called a
Random variables
"... We consider each row as a sample of random variables X1, X2,..., X5. In the cited paper N = 252 samples are given. H.P. Helfrich (University of Bonn) Bayes ’ Statistics Brinkmann School 3 / 19Discrete example Counts Fat / circ. [60,80] (80,100] (100,120] (120,140] (140,160] [0,10] 18 18 0 0 0 (10,2 ..."
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We consider each row as a sample of random variables X1, X2,..., X5. In the cited paper N = 252 samples are given. H.P. Helfrich (University of Bonn) Bayes ’ Statistics Brinkmann School 3 / 19Discrete example Counts Fat / circ. [60,80] (80,100] (100,120] (120,140] (140,160] [0,10] 18 18 0 0 0 (10
Simple Constructions of Almost kwise Independent Random Variables
, 1992
"... We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between the dist ..."
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Cited by 319 (42 self)
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We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1))(log log n + k/2 + log k + log 1 ɛ), where ɛ is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ɛ < 1/(k log n)). An additional advantage of our constructions is their simplicity.
Random forests
 Machine Learning
, 2001
"... Abstract. Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees in the fo ..."
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Cited by 3433 (2 self)
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Abstract. Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees
Continuous Random Variables
"... • Random variables with a continuous range of possible values are quite common – The velocity of a vehicle ..."
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• Random variables with a continuous range of possible values are quite common – The velocity of a vehicle
On the Variance of Fuzzy Random Variables
 Fuzzy Sets and Systems
, 1997
"... This paper deals with an expectation and a realvalued variance of fuzzy random variables. The expectation and the variance of a fuzzy random variable is characterized by Fr'echet's principle in a metric space. We study properties of the variance of a fuzzy random variables and compare it ..."
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Cited by 12 (0 self)
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This paper deals with an expectation and a realvalued variance of fuzzy random variables. The expectation and the variance of a fuzzy random variable is characterized by Fr'echet's principle in a metric space. We study properties of the variance of a fuzzy random variables and compare
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