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Stata Technical Bulletin

sumdist: distribution summary statistics, by quantile group

sumdist estimates distributional summary statistics commonly used by income distribution analysts, complementing those
available via pctile, xtile, and summarize, detail. In fact much of sumdist is a “wrapper” for xtile, combined with
tabdisp to display the results of by-group calculations.

For variable x and distribution function F(x), the statistics provided are

(1) quantiles к = 1, 2,..., m — 1, for m =# quantile groups;

(2) the quantiles expressed as a percentage of medianCr);

(3) the quantile group share of x in total x (group income share, %);

(4) the cumulative quantile group shares of total x (with cumulation in ascending order of .r), i.e., the Lorenz ordinates Z(p)
at each p⅛ =
F{xU for quantile points a⅛; and

(5) the generalized Lorenz ordinates at each p⅛ = F(a⅛), i.e., GL(p⅛) = mean(æ) * L(j>k).

Syntax

sumdist varname [weight] [if exp] [in range] [, ngps(#) qgp(.gpname^)]

fweights and aweights are allowed.

Options

ngps(#) specifies the number of quantile groups. Valid values are integers in the range (0,100]. The default is 10.

qgp gppamee^) creates a new categorical variable, gpname, containing categories summarizing quantile group membership, with
the number of categories equal to
m.

Example

We shall follow a conventional approach and examine the distribution of income amongst all persons in the population,
assuming that each person receives the needs-adjusted income of the household to which s/he belongs. Thus we focus on the
distribution of the variable eybhc weighted by wgt.

A summarize, detail shows some standard features of income distributions, namely significant dispersion combined with
skewness: the mean is well above the median, and there is a long upper tail. (A more sophisticated analysis might consider the
sensitivity of conclusions to differing treatments of the “outlier” largest income.)

. summarize eybhc [fw=wgt], de

Equiv. net income BHC

Percentiles

Smallest

Γ/.

29.04

-123.9898

57.

78.43056

-72.37004

107.

92.24828

-42.89144

Obs

55851705

257.

127.3008

-42.70588

Sum of Wgt.

55851705

507.

194.4472

Mean

233.0179

Largest

Std. Dev.

199.0178

757.

287.2739

1846.438

907.

402.212

2013.499

Variance

39608.08

957.

503.1029

3024.663

Skewness

14.35982

997.

818.264

7740.044

Kurtosis

480.917

Observe the

presence of negative and zero

incomes in the

data. It is up to the user to decide how to handle these. In

general there may be arguments for or against exclusion of them, which vary with circumstances. By default sumdist retains
these values, but they can be excluded using the if option. An example of default output is as follows:



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