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You must know calculus, at least that the integral of xN = 1/(N+1)xN+1 . Define the Pareto distribution as: f(x) = abax-(a+1) or Cx-(a+1) where C = aba (a constant) Remember that the pdf is defined over the domain [b, inf] otherwise zero. Mean = integral xf(x) evaluated from b to infinity. Remember also that the limit of 1/x as x goes to infinity = 0. Similarly for any positive a, (1/x)a goes to 0 as x goes to infinity. mean = integral C x-(a+1)x dx = integral Cx-a = C(1/(-a+1))x-a+1 evaluated over the interval b to infinity. The integral is zero at infinity, so the mean = C(0-1/(-a+1))b-a+1 Remember b-a+1 = b-ab After substituting and cancelling mean = ab/(a-1) for a greater than 1.

Q: How do you derive mean of Pareto distribution?

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The total deviation from the mean for ANY distribution is always zero.

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Related questions

To derive the mean of generalized Pareto distribution you must be good with numbers. You must be good in Calculus, Algebra and Statistics.

The mode of the Pareto distribution is its lowest value.

The total deviation from the mean for ANY distribution is always zero.

Easy. The mean deviation about the mean, for any distribution, MUST be 0.

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The moment generating function for any real valued probability distribution is the expected value of e^tX provided that the expectation exists.For the Type I Pareto distribution with tail index a, this isa*[-x(m)t)^a*Gamma[-a, -x(m)t)] for t < 0, where x(m) is the scale parameter and represents the least possible positive value of X.

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Divakar Sharma has written: 'On some estimators of the parameters of the Pareto distribution'

The Gaussian distribution is the same as the normal distribution. Sometimes, "Gaussian" is used as in "Gaussian noise" and "Gaussian process." See related links, Interesting that Gauss did not first derive this distribution. That honor goes to de Moivre in 1773.

Here is the derivation on dsplog: http://www.dsplog.com/2008/07/17/derive-pdf-rayleigh-random-variable/

Graziella Pareto died in 1973.

Graziella Pareto was born in 1889.