Noun
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.
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. Source: Internet
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. Source: Internet
Relation to other distributions Relation to the exponential distribution The Pareto distribution is related to the exponential distribution as follows. Source: Internet
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). Source: Internet
Pareto types I–IV The Pareto distribution hierarchy is summarized in the next table comparing the survival functions (complementary CDF). Source: Internet
The Gini coefficient for the Pareto distribution is then calculated (for ) to be : (see Aaberge 2005). Source: Internet