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In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
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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.
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Calibration can mean a reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable; [1]
A theory or explanation is hard to vary if all details play a functional role, i.e., cannot be varied or removed without changing the predictions of the theory. Easy to vary (i.e., bad) explanations, in contrast, can be varied to be reconciled with new observations because they are barely connected to the details of the phenomenon of question.
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The theorem, later associated with Frisch, Waugh, and Lovell, and Yule's partial regression notation, were included in chapter 10 of Yule's successful statistics textbook, first published in 1911. The book reached its tenth edition by 1932. [9] In a 1931 paper co-authored with Mudgett, Frisch explicitly quoted Yule's results. [10]