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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 ...
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 .
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 =.
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.
If the two countries' Lorenz curves don't cross, then country A's Lorenz curve is everywhere higher than that of country B, meaning that, for any X from 0 to 100, the poorest X% of the population have a greater national-income-share in country A than in country B.
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 ...
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.
Absorption spectrum of an aqueous solution of potassium permanganate.The spectrum consists of a series of overlapping lines belonging to a vibronic progression. Spectral line shape or spectral line profile describes the form of an electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum.