Search results
Results from the WOW.Com Content Network
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 ...
That g-PDF is plotted with the histogram (black line) and the agreement with the data is very good. Also shown in Figure 2 is a g-PDF curve (red dashed line) for the biased values of T that were used in the previous discussion of bias. Thus the mean of the biased-T g-PDF is at 9.800 − 0.266 m/s 2 (see Table 1).
Taking into account uncertainty arising from different sources, whether in the context of uncertainty analysis or sensitivity analysis (for calculating sensitivity indices), requires multiple samples of the uncertain parameters and, consequently, running the model (evaluating the -function) multiple times. Depending on the complexity of the ...
In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement.An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on.
Confidence bands can be constructed around estimates of the empirical distribution function.Simple theory allows the construction of point-wise confidence intervals, but it is also possible to construct a simultaneous confidence band for the cumulative distribution function as a whole by inverting the Kolmogorov-Smirnov test, or by using non-parametric likelihood methods.
Affine arithmetic is meant to be an improvement on interval arithmetic (IA), and is similar to generalized interval arithmetic, first-order Taylor arithmetic, the center-slope model, and ellipsoid calculus — in the sense that it is an automatic method to derive first-order guaranteed approximations to general formulas.
Frost and Thompson (2000) review several methods for estimating this ratio and hence correcting the estimated slope. [4] The term regression dilution ratio , although not defined in quite the same way by all authors, is used for this general approach, in which the usual linear regression is fitted, and then a correction applied.
Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions.