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The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant ...
In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. Given a sample = ...
The geometric standard deviation is used as a measure of log-normal dispersion analogously to the geometric mean. [3] As the log-transform of a log-normal distribution results in a normal distribution, we see that the geometric standard deviation is the exponentiated value of the standard deviation of the log-transformed values, i.e. = ( ()).
Calculating the geometric mean and then taking the logarithm, statistic S n will be equal to (,) = (()) + + = (() ()) + + (()) + Here only three terms depend on the parameters a and b. Differentiating with respect to those parameters and solving the resulting linear system, the maximum spacing estimates will be
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution of the number X {\displaystyle X} of Bernoulli trials needed to get one success, supported on N = { 1 , 2 , 3 , … } {\displaystyle \mathbb {N} =\{1,2,3,\ldots \}} ;
The power mean could be generalized further to the generalized f-mean: (, …,) = (= ()) This covers the geometric mean without using a limit with f(x) = log(x). The power mean is obtained for f(x) = x p. Properties of these means are studied in de Carvalho (2016).
In mathematics, the arithmetic–geometric mean (AGM or agM [1]) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The arithmetic–geometric mean is used in fast algorithms for exponential , trigonometric functions , and other special functions , as well as some ...