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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.

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Q: How do you derive mean of Pareto distribution?
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Related questions

How do you derive the mean of generalised pareto distribution?

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


How do you derive mode of Pareto Distribution?

The mode of the Pareto distribution is its lowest value.


How do you derive mean deviation from mean for pareto distribution?

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


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How do you derive variance of Pareto distribution?

var(X) = (xm/a - 1)2 a/a-2 . If a < or equal to 2, the variance does not exist.


How do you derive Moment generating function of Pareto distribution?

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.


Derive normal distribution as a limiting case of binomial distribution?

ref veeru


What do you mean by gaussian?

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.


What has the author Divakar Sharma written?

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


What is Pareto distribution?

It is a theoretical probability distribution. I have included two links from the internet which describe the distribution and some of its applications. Sometimes in statistics, we are more interested in the more extreme statistics rather than the average. For example, if we are studying the spread of a disease, perhaps the long distance that the disease can travel one time in 100 is more important than the average distance. Both the exponential and the Pareto distribution are used when the tail end probabilities (cumulative probability close to 1) are of interest. See related links.


How do you derive the rayleigh distribution?

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When was Pareto Group created?

Pareto Group was created in 1986.


When was Graziella Pareto born?

Graziella Pareto was born in 1889.


When did Graziella Pareto die?

Graziella Pareto died in 1973.


What is the population of Pareto Group?

The population of Pareto Group is 2,007.


What is Pareto Group's population?

The population of Pareto Group is 283.


How do you derive the moment generating function of an exponential distribution?

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Both graphs are used to summarize data. Pareto chart is used to establish differences between different groups of data and will assign relative importance to the different groups of data. Histogram is a data distribution graph that will determine if the particular set of data is symmetric or not.


What is pareto superior?

Pareto superior is a state (based on the Pareto criteria) in which one parameter is improved without causing a negative effect on a different parameter.


What is pareto superior and pareto non-comparable?

A state 'A' of the economy is said to be Pareto superior to another state 'B' if at least one person is better off in 'A' than in B' but none is worse off . If there is no transitive relationship between the points then we have Pareto non-comparability. If neither A is Pareto superior to B nor B superior to A then we have Pareto non-comparability for the states of economy.


What do we mean by pareto optimality?

Pareto Optimality is an economic situation used to refer to a state wherby resources within the economy are distributed in such a way that some group of individuals are better off than some.


What is Vilfredo Pareto's birthday?

Vilfredo Pareto was born on July 15, 1848.


When was Vilfredo Pareto born?

Vilfredo Pareto was born on July 15, 1848.


What is Paula Pareto's birthday?

Paula Pareto was born on January 16, 1986.


When was Paula Pareto born?

Paula Pareto was born on January 16, 1986.