{smcl}
{* 13Feb2007}{...}
{cmd:help fastgini}
{hline}
{title:Title}
{p2colset 8 20 22 2}{...}
{p2col :{hi:fastgini} {hline 2}}Fast algorithm for calculation of Gini coefficient and it's jackknife standard
errors{p_end} {p2colreset}{...}
{title:Syntax}
{p 8 16 2}
{cmd:fastgini} {varname} {ifin} {weight} [{cmd:,} {opt bin(#)} {opt jk} {opt L:evel(#)} {opt noch:eck}]
{p 4 6 2}
{opt pweight}s and {opt fweight}s are allowed; see {help weight}.{p_end}
{title:Description}
{pstd}
{cmd:fastgini} calculates the Gini coefficient for either unit-level or aggregated level data. Optionally
it returns the jackknife estimates of the standard error. {cmd:fastgini} uses a fast optimized algorithm
that could be especially useful when calculating the Gini coefficient and it's standard errors for the large samples.
The command implements algorithms for both exact and approximate calculation of the Gini coefficient.
{dlgtab:Main}
{phang}
{opt bin(#)} set number of bins. Specifying this option can dramatically reduce the computation time when working with
large datasets (1M+ obs). When {opt bin(#)} is specified {cmd:fastgini} uses approximation algorithm for Gini
calculation. Specifying the sufficient number bins allows obtaining the approximation for the Gini at any desired level
of precision. For example, on the dataset of 1,000,000 observations {opt bin(100,000)} will in most
cases estimate computer-exact value of Gini. This calculation required significantly less computer time compared to the
exact estimation of the Ginin on whole sample.
{phang}
{opt jk} estimate jackknife (leave-one-out) standard error of the Gini coefficient. An efficient method of calculating
jackknife estimates involves only two (one to get the Gini coefficient itself and another for standard errors)
runs through the data.
{phang}
{opt level(#)} set confidence level for the reported jackknife confidence intervals; default is {opt level(95)}.
{phang}
{opt nocheck} by default, non-positive values of {it:varname} are excluded from Gini calculations. Specifying {opt
nocheck} skips the value check as well as ignores {ifin} conditions. The option can be useful to speed-up the
execution if {cmd:fastgini} is used within loops.
{title:Saved Results}
{phang}{cmd:fastgini} saves in {cmd:r()}:
{p 8 4 2}{cmd:r(gini)} calculated Gini coefficient;
{phang} if {opt jk} option specified:
{p 8 4 2}{cmd:r(se)} jackknife estimate for the standard error of the Gini;
{p 8 4 2}{cmd:r(mse)} jackknife estimate for the mean standard error of the Gini;
{p 8 4 2}{cmd:r(gini_jk)} jackknife estimate for the Gini.
{title:Remarks}
{phang}{cmd:fastgini} uses formula:
i=N j=i
SUM W_i*(SUM W_j*X_j - W_i*X_i/2)
i=1 j=1
G = 1 - 2* ----------------------------------
i=N i=N
SUM W_i*X_i * SUM W_i
i=1 i=1
{pmore}where observations are sorted in ascending order of X.
{phang}if {opt bin(M)} is specified, the data are aggregated into {it:M} equal-size bins, i.e.
~
X_i = (X_min + i * binsize) binsize = (X_max - X_min)/M
~ ~ ~
W_i = SUM W_j (if X_(i-1)<=X_j