help mata mm_gini()
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Title

    mm_gini() -- Gini coefficient


Syntax

        real rowvector mm_gini(X [, w])

    where

            X:  real matrix containing data (rows are observations, columns
                variables)

            w:  real colvector containing weights


Description

    mm_gini(X, w) returns the Gini coefficient of each column of X.

    w specifies the weights. Omit w, or specify w as 1 to obtain unweighted
    results. Missing values in X or w are omitted from the calculation.


Remarks

    The formula used in mm_gini() is

        G(x) = 2 * Cov0(x, F) / mu

    where mu is the mean of x. Let N denote the number of observations (or
    sum of weights). Then,

        Cov0(x, F) = DCP(x, F) / N

    where DCP(x, F) denotes the deviation cross product between x and its
    (adjusted) empirical cumulative, F. To be precise, F is defined as

               1                     w_i
        F_i =  - * (    SUM  w_j  -  --- ),  i = 1,...,n
               W     x_j<=x_i         2

    where w_i are weights and W is the total sum of weights.

    Example:

        : x = exp(invnormal(uniform(100,1)))
        
        : mm_gini(x, 1)
          .5158638536


Conformability

    mm_gini(x, w):
           X:  n x k
           w:  n x 1 or 1 x 1
      result:  1 x k


Diagnostics

    None.


Source code

    mm_gini.mata

Author

    Ben Jann, ETH Zurich, jann@soz.gess.ethz.ch


Also see

    Online:  help for [M-5] mean(), moremata

    Links to user-written programs:  anogi, egen_inequal, inequal7, ineqerr,