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The equally distributed welfare equivalent income associated with an Atkinson Index with an inequality aversion parameter of 1.0 is simply the geometric mean of incomes. For values other than one, the equivalent value is an Lp norm divided by the number of elements, with p equal to one minus the inequality aversion parameter.
The output image G(x,y) of a geometric mean is given by (,) = [, (,)] Where S(x,y) is the original image, and the filter mask is m by n pixels. Each pixel of the output image at point (x,y) is given by the product of the pixels within the geometric mean mask raised to the power of 1/mn.
The second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. If all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean. [1]
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 ...
This estimate is sometimes referred to as the "geometric CV" (GCV), [19] [20] due to its use of the geometric variance. Contrary to the arithmetic standard deviation, the arithmetic coefficient of variation is independent of the arithmetic mean. The parameters μ and σ can be obtained, if the arithmetic mean and the arithmetic variance are known:
These DNA kits for dogs give you way more information than your dog’s breed composition. Many of the kits can be upgraded to include more health and trait testing or allergy and age tests.
The values for which both likelihood and spacing are maximized, the maximum likelihood and maximum spacing estimates, are identified. Suppose two values x (1) = 2, x (2) = 4 were sampled from the exponential distribution F(x;λ) = 1 − e −xλ, x ≥ 0 with unknown parameter λ > 0. In order to construct the MSE we have to first find the ...
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. = ( ()).