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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 attractor is difficult to analyze, but the action of the differential equation on the attractor is described by a fairly simple geometric model. [24] Proving that this is indeed the case is the fourteenth problem on the list of Smale's problems. This problem was the first one to be resolved, by Warwick Tucker in 2002. [25]
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 ...
The population, but the Lorenz Curve (discussed in the Gini section) graphs the cumulative income of the bottom-income x% of the population, for all x from 0 to 100. However, when commenting on the data, it can be expressed as the inverse, showing the percentage of income of the wealthiest x %.
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
The graph of the logistic map + = is the plane curve that plots the relationship between and +, with (or x) on the horizontal axis and + (or f (x)) on the vertical axis. The graph of the logistic map looks like this, except for the case r = 0:
The Lorenz curve was taken up by the American statistician Max Lorenz to study the income problem. In the Lorenz curve method, firstly, the number of consumer units in various income brackets and their income is evaluated. They are then divided into percentages that rank the consumer units from the lowest to the highest income.
The Lorenz curve is convexe and not concave as is said in the text, see the graph below. Can we get a real life example for the illustration from some place? Paranoid 20:10, 6 Jan 2005 (UTC) The Lorenz Curve is used in geography as well to represent unequal distribution of the world's population over area...please add that in