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A practical example of a Lorenz curve: the Lorenz curves of Denmark, Hungary, and Namibia. A Lorenz curve always starts at (0,0) and ends at (1,1). The Lorenz curve is not defined if the mean of the probability distribution is zero or infinite. The Lorenz curve for a probability distribution is a continuous function. However, Lorenz curves ...
The Lorenz curve is used to describe the inequality in the distribution of a quantity (usually income or wealth in economics, or size or reproductive output in ecology). The most common summary statistic for the Lorenz curve is the Gini coefficient, which is an overall measure of inequality within the population.
A set of data that arises from the log-normal distribution has a symmetric Lorenz curve (see also Lorenz asymmetry coefficient). [ 32 ] The harmonic H {\displaystyle H} , geometric G {\displaystyle G} and arithmetic A {\displaystyle A} means of this distribution are related; [ 33 ] such relation is given by
This curve is an orbit of the transformation. The form of the rational invariants shows that these flowlines (orbits) have a simple description: suppressing the inessential coordinate y , each orbit is the intersection of a null plane , t = z + c 2 , with a hyperboloid , t 2 − x 2 − z 2 = c 3 .
the Lorenz curve, a graphical representation of the inequality in a quantity's distribution This page was last edited on 27 December 2020, at 04:47 (UTC). Text is ...
Lorenz Curve: A graphical representation of income distribution, where a perfectly straight line (45-degree line) reflects absolute equality. Quintile and Decile Ratios: These divide the population into equal parts (quintiles - fifths, deciles - tenths) to compare the income shares received by each group.
The derivative of any smooth curve C(t) with C(0) = I in the group depending on some group parameter t with respect to that group parameter, evaluated at t = 0, serves as a definition of a corresponding group generator G, and this reflects an infinitesimal transformation away from the identity.
In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. The term " butterfly effect " in popular media may stem from the real-world implications of the Lorenz attractor, namely that tiny changes in initial conditions evolve to completely different trajectories .