Search results
Results from the WOW.Com Content Network
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 ...
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 .
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.
The Gini coefficient is a measure of the deviation of the Lorenz curve from the equidistribution line which is a line connecting [0, 0] and [1, 1], which is shown in black (α = ∞) in the Lorenz plot on the right. Specifically, the Gini coefficient is twice the area between the Lorenz curve and the equidistribution line.
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 Lorenz curve, a graphical representation of the inequality in a quantity's distribution Topics referred to by the same term This disambiguation page lists articles associated with the title Lorentz curve .
Sometimes the entire Lorenz curve is not known, and only values at certain intervals are given. In that case, the Gini coefficient can be approximated using various techniques for interpolating the missing values of the Lorenz curve. If (X k, Y k) are the known points on the Lorenz curve, with the X k indexed in increasing order (X k – 1 < X ...
A set of data that arises from the log-normal distribution has a symmetric Lorenz curve (see also Lorenz asymmetry coefficient). [32] The harmonic , geometric and arithmetic means of this distribution are related; [33] such relation is given by =.