As q approaches infinity, the generalized mean approaches the maximum value.

The second approach is to calculate the species diversity for each subunit separately, and then take a weighted generalized mean of these.

Replacing the arithmetic and harmonic mean by a pair of generalized means of opposite, finite exponents yields the same result.

The generalized mean, also known as the power mean or Hölder mean, is an abstraction of the quadratic, arithmetic, geometric and harmonic means.

In mathematics, generalized means are a family of functions for aggregating sets of numbers, that include as special cases the arithmetic, geometric, and harmonic means.

The denominator equals average proportional abundance of the types in the dataset as calculated with the weighted generalized mean with exponent q - 1.

The generalized mean is also known as power mean or Hölder mean (named after Otto Hölder).

With some values of the parameter q, the generalized mean with exponent q - 1 gives familiar kinds of mean as special cases.

This is a generalization of the inequality of arithmetic and geometric means and a special case of an inequality for generalized means.

This corresponds to the weighted generalized mean of the values when q approaches infinity, and hence equals the inverse of true diversity of order infinity (1/D).

As q approaches infinity, the generalized mean with exponent q - 1 approaches the maximum value, which is the proportional abundance of the most abundant species in the dataset.

The true diversity in a dataset is calculated by first taking the weighted generalized mean of the proportional abundances of the types in the dataset, and then taking the inverse of this.

His formidable list of teachers included Milton Babbitt and Charles Wuorinen, from whom he absorbed the 12-tone technique but, as he explained, as "a generalized means of expression rather than a way to compose."

The "Nonlinear Order Statistics Filters" were introduced, a special case of which are linear median, order statistics, homomorphic, a-trimmed median, generalized mean, nonlinear mean and fuzzy nonlinear filters.

Like most means, the generalized mean is a homogeneous function of its arguments x, ..., x. That is, if b is a positive real number, then the generalized mean with exponent p of the numbers is equal to b times the generalized mean of the numbers x, .