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Downloadable EXCEL program for the determination of the Most Probable Numbers (MPN), their standard deviations, confidence bounds and rarity values according to Jarvis, B., Wilrich, C., and P.-T. Wilrich: Reconsideration of the derivation of Most Probable Numbers, their standard deviations, confidence bounds and rarity values.
A standard choice of uninformative prior for this problem is the Jeffreys prior, () /, which is equivalent to adopting a rescaling-invariant flat prior for ln(σ 2). One consequence of adopting this prior is that S 2 /σ 2 remains a pivotal quantity , i.e. the probability distribution of S 2 /σ 2 depends only on S 2 /σ 2 , independent of the ...
For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%. Shown percentages are rounded theoretical probabilities intended only to approximate the empirical ...
Bias in standard deviation for autocorrelated data. The figure shows the ratio of the estimated standard deviation to its known value (which can be calculated analytically for this digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be
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The Yamartino method, introduced by Robert J. Yamartino in 1984, solves both problems [2] A further discussion of the Yamartino method, along with other methods of estimating the standard deviation of wind direction can be found in Farrugia & Micallef. It is possible to calculate the exact standard deviation in one pass.
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In law, a presumption is an "inference of a particular fact". [1] There are two types of presumptions: rebuttable presumptions and irrebuttable (or conclusive) presumptions. [2]: 25 A rebuttable presumption will either shift the burden of production (requiring the disadvantaged party to produce some evidence to the contrary) or the burden of proof (requiring the disadvantaged party to show the ...