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The base-10 logarithm of a normalized number (i.e., a × 10 b with 1 ≤ a < 10 and b as an integer), is rounded such that its decimal part (called mantissa) has as many significant figures as the significant figures in the normalized number. log 10 (3.000 × 10 4) = log 10 (10 4) + log 10 (3.000) = 4.000000...
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
The uncertainty theory invented by Baoding Liu [1] is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. [ clarification needed ]
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Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
Essentially, the mean is the location of the PDF on the real number line, and the variance is a description of the scatter or dispersion or width of the PDF. To illustrate, Figure 1 shows the so-called Normal PDF , which will be assumed to be the distribution of the observed time periods in the pendulum experiment.
Probability bounds analysis gives the same answer as interval analysis does when only range information is available. It also gives the same answers as Monte Carlo simulation does when information is abundant enough to precisely specify input distributions and their dependencies. Thus, it is a generalization of both interval analysis and ...
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.