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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 .
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
When the mean of a probability distribution function (PDF) is undefined, no one can compute a reliable average over the experimental data points, regardless of the sample's size. Note that the Cauchy principal value of the mean of the Cauchy distribution is lim a → ∞ ∫ − a a x f ( x ) d x {\displaystyle \lim _{a\to \infty }\int _{-a}^{a ...
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 .
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 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.