The Chernoff bound gives an estimate for this probability. Its numerical value can be found using the rate function for the exponential distribution and evaluate enIExp(x/n)=e-10IExp(30/10), or using the rate function for the Erlang distribution directly, eIErl(x)=e-IErl(30). Both ...
In summary, the Chernoff Bound for Binomial Distribution is a mathematical tool used to estimate the probability of deviation from expected value in a large number of independent and identically distributed random variables. It is calculated using the Chernoff-Hoeffding inequality and takes into account...
We propose a Chernoff-bound approach and examine standard deviation value to enhance the accuracy of the existing fast incremental model tree with the drift detection (FIMT-DD) algorithm. It is a data stream mining algorithm that can observe and form a m
An optimal recursive algorithm for Chernoff bound feature selection of multiclass problem and normal multidistribution oriented is presented. This algorithm is twofold. Setting the parameter 's' in the feature and original space, the optimal solution of transformation matrix can be found. The optimal...
An interesting result from the point of view of upper variance bounds is the inequality of Chernoff [Chernoff, H., 1981. A note on an inequality involving the normal distribution. Annals of Probability 9, 533–535]. Namely, that for every absolutely continuous function g with derivative g ′...
σ approaches a standard normal distribution N (0, 1). Thus, as n →∞, for any ?xed β > 0 we have 1 Pr[|X ? ?| > βσ] →√ ∞ e? t2 2 dt ≈ 1 √ e? β2 2 . 2π β 2πβ Note that the probability of a β-deviation from the mean (in units of the standard...
Probability Bounds, Multivariate Normal Distribution and an Integro-Differential Inequality for Random Vectors In the light of an inequality derived by Chernoff (1981), a characterization of the normal distribution was obtained by Borovkov and Utev (1983). Prakasa Rao and Sreehari (1986) derived a...