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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.
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 H {\displaystyle H} , geometric G {\displaystyle G} and arithmetic A {\displaystyle A} means of this distribution are related; [ 33 ] such relation is given by
Max Otto Lorenz (/ ˈ l ɒr ən t s / LORR-ənts; September 19, 1876 – July 1, 1959) was an American economist who developed the Lorenz curve in an undergraduate essay. [1] He published a paper on this when he was a doctoral student at the University of Wisconsin–Madison . [ 2 ]
The pseudo-Voigt profile (or pseudo-Voigt function) is an approximation of the Voigt profile V(x) using a linear combination of a Gaussian curve G(x) and a Lorentzian curve L(x) instead of their convolution. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes.
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 .
The intersections of this curve and the 45° line are points that satisfy equation (3-4), so the intersections represent fixed points and 2-periodic points. If we draw a graph of the logistic map f 2 ( x ) {\displaystyle f^{2}(x)} , we can observe that the slope of the tangent at the fixed point x f 2 {\displaystyle x_{f2}} exceeds 1 at the ...