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MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral
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 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).
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 ...
The inverse x(F) may not exist because the cumulative distribution function has intervals of constant values. However, the previous formula can still apply by generalizing the definition of x(F): = {: ()} where inf is the infimum. For an example of a Lorenz curve, see Pareto distribution.
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.
The Theil index is a statistic primarily used to measure economic inequality [1] and other economic phenomena, though it has also been used to measure racial segregation. [2] [3] The Theil index T T is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy.
Since all the inequalities are in the same form (all less-than or all greater-than), we can examine the coefficient signs for each variable. Eliminating x would yield 2*2 = 4 inequalities on the remaining variables, and so would eliminating y. Eliminating z would yield only 3*1 = 3 inequalities so we use that instead.