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A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij–Petunin inequality ...
For any given event, only one of two possibilities may hold: It occurs or it does not. The relative frequency of occurrence of an event, observed in a number of repetitions of the experiment, is a measure of the probability of that event. This is the core conception of probability in the frequentist interpretation.
In probability theory and statistics, a stochastic order quantifies the concept of one random variable being "bigger" than another. These are usually partial orders, so that one random variable may be neither stochastically greater than, less than, nor equal to another random variable . Many different orders exist, which have different ...
Stochastic dominance is a partial order between random variables. [1] [2] It is a form of stochastic ordering.The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Non-sampling errors are much harder to quantify than sampling errors. [2] Non-sampling errors in survey estimates can arise from: [3] Coverage errors, such as failure to accurately represent all population units in the sample, or the inability to obtain information about all sample cases; Response errors by respondents due for example to ...
In probability theory and statistics, two real-valued random variables, , , are said to be uncorrelated if their covariance, [,] = [] [] [], is zero. If two variables are uncorrelated, there is no linear relationship between them.