the mean of a function is loosely defined as the ”average" value of the function over its domain. In a one-dimensional domain, the mean of a function f(x)...

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several...

as the quadratic mean (denoted M 2 {\displaystyle M_{2}} ), a special case of the generalized mean. The RMS of a continuous function is denoted f R M...

mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that...

geometric mean, using a function f {\displaystyle f} . It is also called Kolmogorov mean after Soviet mathematician Andrey Kolmogorov. It is a broader generalization...

mean ( /ˌærɪθˈmɛtɪk/ arr-ith-MET-ik), arithmetic average, or just the mean or average is the sum of a collection of numbers divided by the count of numbers...

geometric mean of the future exchange rates, or more generally a product of the weighted geometric mean and a so-called reciprocity function. The weights of the...

analysis in mathematics, a function of bounded mean oscillation, also known as a BMO function, is a real-valued function whose mean oscillation is bounded...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

the concept of a mean-periodic function is a generalization introduced in 1935 by Jean Delsarte of the concept of a periodic function. Further results...

of a function may refer either to the codomain of the function, or the image of the function. In some cases the codomain and the image of a function are...

mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R , {\displaystyle f\colon...

mathematics, generalised means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include as special...

gave a method of constructing Haar measure using mean values of functions, though it only works for compact groups. The idea is that given a function f {\displaystyle...

related error function erf ⁡ ( x ) {\textstyle \operatorname {erf} (x)} gives the probability of a random variable, with normal distribution of mean 0 and variance...

{1}{\lambda }}.} The mean lifetime can be looked at as a "scaling time", because the exponential decay equation can be written in terms of the mean lifetime, τ...

{\displaystyle F_{2,1}} is a hypergeometric function. This function is also known as Barnes's extended hypergeometric function. The definition of F N , D ( n , d...

of the shape parameters of a beta distribution are (in general) a complicated function of the sample geometric mean, and of the sample geometric mean...

mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This...

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures...

} ⁠ of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function ⁠ exp...

mathematics, a contraharmonic mean (or antiharmonic mean) is a function complementary to the harmonic mean. The contraharmonic mean is a special case of the Lehmer...

"useful life period". The mean time between failures (MTBF, 1 / λ {\displaystyle 1/\lambda } ) is often reported instead of the failure rate, as numbers...

Mean shift is a non-parametric feature-space mathematical analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm...

continuous). Generally, the term smooth function refers to a C ∞ {\displaystyle C^{\infty }} -function. However, it may also mean "sufficiently differentiable"...

probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value...

For example, the cumulative distribution function of Exponential(λ) (i.e. intensity λ and expected value (mean) 1/λ) is F ( x ; λ ) = { 1 − e − λ x x ≥...

value of a concave function of an arithmetic mean is greater than or equal to the arithmetic mean of the function's values. Since the logarithm function is...

most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum...

undefined, and thus so is the mean. When the mean of a probability distribution function (PDF) is undefined, no one can compute a reliable average over the...