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Toggle Statistics subsection. 9.1 Sample distributions of mean and variance. ... In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means.
The harmonic law is the only one two-parameter family of distributions that is closed under change of scale and under reciprocals, such that the maximum likelihood estimator of the population mean is the sample mean (Gauss' principle). [3] In 1946, Halphen realized that introducing an additional parameter, flexibility could be improved.
The data type is a fundamental concept in statistics and controls what sorts of probability distributions can logically be used to describe the variable, the permissible operations on the variable, the type of regression analysis used to predict the variable, etc.
Examples of measures that are a combination of precision and recall are the F-measure (the weighted harmonic mean of precision and recall), or the Matthews correlation coefficient, which is a geometric mean of the chance-corrected variants: the regression coefficients Informedness (DeltaP') and Markedness (DeltaP).
Subcontrary, which we call harmonic, is the mean when they are such that, by whatever part of itself the first term exceeds the second, by that part of the third the middle term exceeds the third. It turns out that in this proportion the interval between the greater terms is greater and that between the lesser terms is less.
The harmonic mean is an average which is useful for sets of numbers which are defined in relation to some unit, as in the case of speed (i.e., distance per unit of time): ¯ = (=) For example, the harmonic mean of the five values: 4, 36, 45, 50, 75 is
The weighted harmonic mean of p-values , …, is defined as = = = /, where , …, are weights that must sum to one, i.e. = =.Equal weights may be chosen, in which case = /.. In general, interpreting the HMP directly as a p-value is anti-conservative, meaning that the false positive rate is higher than expected.
There is a one-parameter family of statistics, with parameter β, which determines the relative weights of precision and recall. The traditional or balanced F-score is the harmonic mean of precision and recall: