{smcl} {* 26mar2008}{...} {cmd:help mata mm_gini()} {hline} {title:Title} {pstd} {bf:mm_gini() -- Gini coefficient} {title:Syntax} {p 8 12 2} {it:real rowvector} {cmd:mm_gini(}{it:X} [{cmd:,} {it:w}]{cmd:)} {p 4 4 2} where {p 12 16 2} {it:X}: {it:real matrix} containing data (rows are observations, columns variables) {p 12 16 2} {it:w}: {it:real colvector} containing weights {title:Description} {pstd} {cmd:mm_gini(}{it:X}{cmd:,} {it:w}{cmd:)} returns the Gini coefficient of each column of {it:X}. {pstd} {it:w} specifies the weights. Omit {it:w}, or specify {it:w} as 1 to obtain unweighted results. Missing values in {it:X} or {it:w} are omitted from the calculation. {title:Remarks} {pstd}The formula used in {cmd:mm_gini()} is G(x) = 2 * Cov0(x, F) / mu {pstd}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 {pstd}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 {pstd}where w_i are weights and W is the total sum of weights. {pstd} Example: {com}: x = exp(invnormal(uniform(100,1))) {res} {com}: mm_gini(x, 1) {res} .5158638536{txt} {title:Conformability} {pstd} {cmd:mm_gini(}{it:x}{cmd:,} {it:w}{cmd:)}: {p_end} {it:X}: {it:n x k} {it:w}: {it:n x 1} or {it:1 x 1} {it:result}: {it:1 x k} {title:Diagnostics} {pstd}None. {title:Source code} {pstd} {help moremata_source##mm_gini:mm_gini.mata} {title:Author} {pstd} Ben Jann, University of Bern, jann@soz.unibe.ch {title:Also see} {psee} Online: help for {bf:{help mf_mean:[M-5] mean()}}, {bf:{help moremata}} {p_end} {psee} Links to user-written programs: {net "describe anogi, from(http://fmwww.bc.edu/RePEc/bocode/a)":anogi}, {net "describe egen_inequal, from(http://fmwww.bc.edu/RePEc/bocode/e)":egen_inequal}, {net "describe inequal7, from(http://fmwww.bc.edu/RePEc/bocode/i)":inequal7}, {net "describe sg115, from(http://www.stata.com/stb/stb51)":ineqerr}, {net "describe ginidesc, from(http://fmwww.bc.edu/RePEc/bocode/g)":ginidesc}, {net "describe descogin, from(http://fmwww.bc.edu/RePEc/bocode/d)":descogin}, {net "describe ineqdeco, from(http://fmwww.bc.edu/RePEc/bocode/i)":ineqdeco}, {net "describe ineqdec0, from(http://fmwww.bc.edu/RePEc/bocode/i)":ineqdec0}