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[1] [2] Also dating from the latter half of the 19th century, the inequality attributed to Chebyshev described bounds on a distribution when only the mean and variance of the variable are known, and the related inequality attributed to Markov found bounds on a positive variable when only the mean is known.
Chebyshev's inequality requires the following information on a random variable : . The expected value [] is finite.; The variance [] = [( [])] is finite.; Then, for every constant >,
P(at least one estimation is bad) = 0.05 ≤ P(A 1 is bad) + P(A 2 is bad) + P(A 3 is bad) + P(A 4 is bad) + P(A 5 is bad) One way is to make each of them equal to 0.05/5 = 0.01, that is 1%. In other words, you have to guarantee each estimate good to 99%( for example, by constructing a 99% confidence interval) to make sure the total estimation ...
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution.Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range.
Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability , to describe how likely an event is to occur, this method uses two numbers: the upper probability of the event and the lower probability of the event.
Decision boundaries can be approximations of optimal stopping boundaries. [ 2 ] The decision boundary is the set of points of that hyperplane that pass through zero. [ 3 ] For example, the angle between a vector and points in a set must be zero for points that are on or close to the decision boundary.