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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 ...
The statistical errors, on the other hand, are independent, and their sum within the random sample is almost surely not zero. One can standardize statistical errors (especially of a normal distribution ) in a z-score (or "standard score"), and standardize residuals in a t -statistic , or more generally studentized residuals .
When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are "errors" in the sense in which that term is used in statistics; see errors and residuals in statistics.
Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results. In order to make a simulation statistically efficient, i.e., to obtain a greater precision and smaller confidence intervals for the output random variable of interest, variance reduction techniques can be used ...
The bias is a fixed, constant value; random variation is just that – random, unpredictable. Random variations are not predictable but they do tend to follow some rules, and those rules are usually summarized by a mathematical construct called a probability density function (PDF). This function, in turn, has a few parameters that are very ...
THERP is a first-generation methodology, which means that its procedures follow the way conventional reliability analysis models a machine. [3] The technique was developed in the Sandia Laboratories for the US Nuclear Regulatory Commission. [4]
The summary statistics is particularly useful and popular when used to evaluate models where the dependent variable is binary, taking on values {0,1}. Example [ edit ]
Generally Bessel's correction is an approach to reduce the bias due to finite sample size. Such finite-sample bias correction is also needed for other estimates like skew and kurtosis, but in these the inaccuracies are often significantly larger. To fully remove such bias it is necessary to do a more complex multi-parameter estimation.