Pareto distribution
Noun
Meaning
Pareto distribution (plural Pareto distributions)
(statistics) A probability distribution such that for a random variable X with that distribution holds that the probability that X is greater than some number x is given by
Pr
(
X
>
x
)
=
(
x
x
m
)
−
k
{\displaystyle \Pr(X>x)=\left({\frac {x}{x_{\mathrm {m} }}}\right)^{-k}}
for all x ≥ xm, where xm is the (necessarily positive) minimum possible value of X, and k is a positive parameter.
Synonyms
Examples
Kleiber and Kotz (2003): page 94. citation * In hydrology the Pareto distribution is applied to extreme events such as annually maximum one-day rainfalls and river discharges.
Pareto Q-Q plots compare the quantiles of the log-transformed data to the corresponding quantiles of an exponential distribution with mean 1 (or to the quantiles of a standard Pareto distribution) by plotting the former versus the latter.
Relation to other distributions Relation to the exponential distribution The Pareto distribution is related to the exponential distribution as follows.
Income is distributed according to a power-law known as the Pareto distribution (for example, the net worth of Americans is distributed according to a power law with an exponent of 2).
Pareto types I–IV The Pareto distribution hierarchy is summarized in the next table comparing the survival functions (complementary CDF).
The Gini coefficient for the Pareto distribution is then calculated (for ) to be : (see Aaberge 2005).