Pointwise 95 % confidence bands, and simultaneous 95 % confidence bands constructed using Scheff?s method are shown.
12.
Pointwise 95 % confidence bands, and simultaneous 95 % confidence bands constructed using Scheff?s method are shown.
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Confidence bands for simulated data depicting the proportion of voters supporting a given candidate in election, as a function of the voters'ages.
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Point-wise or simultaneous confidence bands can then be used to provide a sense of the uncertainty in the estimate of the regression function.
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A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data.
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It can be shown that at confidence level ( 1 " " ? " ) the confidence band has hyperbolic form given by the equation
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Another alternative to the Working Hotelling Scheff?band is the Gavarian band, which is used when a confidence band is needed that maintains equal widths at all levels.
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The blue picture illustrates an example of fitting the Gumbel distribution to ranked maximum one-day October rainfalls showing also the 90 % confidence band based on the binomial distribution.
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The value " f " is referred to as the number of falsetickers, those sources which are in error ( the actual value is outside the confidence band ).
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If the software program does not generate the confidence band, it is approximately \ pm 2 / \ sqrt { N }, with " N " denoting the sample size.
