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A more frequently encountered inequality measure is the Gini coefficient which is based on the summation, over all income-ordered population-percentiles, of the cumulative income up to each percentile. That sum is divided by the maximum value that it could have (its value with complete equality), to express it as a percentage of its maximum ...
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Free add-on to STATA to compute inequality and poverty measures; Free Online Software (Calculator) computes the Gini Coefficient, plots the Lorenz curve, and computes many other measures of concentration for any dataset; Free Calculator: Online and downloadable scripts (Python and Lua) for Atkinson, Gini, and Hoover inequalities
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).
Given: a function f : A R from some set A to the real numbers Search for: an element x 0 in A such that f(x 0) ≤ f(x) for all x in A. In continuous optimization, A is some subset of the Euclidean space R n, often specified by a set of constraints, equalities or inequalities that the members of A have to satisfy.
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
The MLD of household income has been defined as [1] = = ¯ where N is the number of households, is the income of household i, and ¯ is the mean of .Naturally the same formula can be used for positive variables other than income and for units of observation other than households.
The line that determines the half-planes (ax + by = c) is not included in the solution set when the inequality is strict. A simple procedure to determine which half-plane is in the solution set is to calculate the value of ax + by at a point (x 0, y 0) which is not on the line and observe whether or not the inequality is satisfied.