In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for...

numbers. The geometric mean is one of the three classical Pythagorean means, together with the arithmetic mean and the harmonic mean. For all positive data...

mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0 = x and h0 = y...

Arithmetic-geometric mean Arithmetic-harmonic mean Cesàro mean Chisini mean Contraharmonic mean Elementary symmetric mean Geometric-harmonic mean Grand mean Heinz mean Heronian...

case, besides the harmonic mean HX based on the random variable X, also another harmonic mean appears naturally: the harmonic mean based on the linear...

mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor...

The harmonic mean p-value (HMP) is a statistical technique for addressing the multiple comparisons problem that controls the strong-sense family-wise...

Hermann Karcher. On the real numbers, the arithmetic mean, median, geometric mean, and harmonic mean can all be interpreted as Fréchet means for different...

\dots } Harmonic numbers are related to the harmonic mean in that the n-th harmonic number is also n times the reciprocal of the harmonic mean of the first...

a contraharmonic mean is a function complementary to the harmonic mean. The contraharmonic mean is a special case of the Lehmer mean, L p {\displaystyle...

mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean...

classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions...

sequence of harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider...

for the i-th query. The reciprocal value of the mean reciprocal rank corresponds to the harmonic mean of the ranks. Suppose we have the following three...

the harmonic series after the first is the harmonic mean of the neighboring terms, so the terms form a harmonic progression; the phrases harmonic mean and...

_{p\to -\infty }M_{p}(x_{1},\dots ,x_{n})=\min\{x_{1},\dots ,x_{n}\}} harmonic mean M − 1 ( x 1 , … , x n ) = n 1 x 1 + ⋯ + 1 x n {\displaystyle M_{-1}(x_{1}...

{1}{n}}\cdot \sum {\frac {p_{0}}{p_{t}}}}}} Is the geometric mean of the Carli and the harmonic price indexes. In 1922 Fisher wrote that this and the Jevons...

F-measure (the weighted harmonic mean of precision and recall), or the Matthews correlation coefficient, which is a geometric mean of the chance-corrected...

arithmetic progression. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. As a third equivalent...

The geometric mean (G) is G = x m exp ⁡ ( 1 α ) . {\displaystyle G=x_{\text{m}}\exp \left({\frac {1}{\alpha }}\right).} The harmonic mean (H) is H = x...

include "harmonic" include: Projective harmonic conjugate Cross-ratio Harmonic analysis Harmonic conjugate Harmonic form Harmonic function Harmonic mean Harmonic...

sensitivity in diagnostic binary classification. The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision...

In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square. Given a set x i {\displaystyle...

exponent greater than 1. However, it is larger than the geometric mean and the harmonic mean, respectively. The inequalities are strict unless both numbers...

1080/01621459.1942.10500636 Average Central tendency Summary statistics Weighted arithmetic mean Weighted harmonic mean Non-Newtonian calculus website v t e...

dispense with this condition and are thus more generally valid. The harmonic mean p-value (HMP) procedure provides a multilevel test that improves on...

1/y) = xy/M(x,y). The arithmetic–harmonic mean is equivalent to the geometric mean. The arithmetic–geometric mean can be used to compute – among others...

types of means, such as geometric and harmonic. In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology...

f-mean corresponds to the harmonic mean. If I = R + {\displaystyle I=\mathbb {R} ^{+}} and f ( x ) = x p {\displaystyle f(x)=x^{p}} , then the f-mean corresponds...

The harmonic mean of a and b is 2 1 a + 1 b {\displaystyle {\tfrac {2}{{\frac {1}{a}}+{\frac {1}{b}}}}} or 2c. In other words, c is half the harmonic mean...