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help for moments2
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Moment-based statistics

        moments2 [varlist] [if exp] [in range] [weight] [, type(name) allobs
                 format(numeric_format(s)) matname(matrix_name)
                 tabdisp_options variablenames ]

        moments2 varname [if exp] [in range] [weight] [, type(name) allobs
                 by(varlist) format(numeric_format(s)) matname(matrix_name)
                 tabdisp_options ]

    by ... : may be used with moments2; see help on by.

    aweights and fweights are allowed; see help weights.


Description

    moments2 calculates mean, standard deviation, skewness and kurtosis of
    type() for varlist. Any string variables in varlist are ignored.
    Definitions and a discussion of the measures specified by type() can be
    found in: Joanes, D. N. & Gill, C. A. (1998). Comparing measures of
    sample skewness and kurtosis. The Statistician, 47, 183-189.


Options

    type() (default: type(G)) specifies the type of skewness and kurtosis
        measure as follows [mr = sum((xi-mean(X))^r)/n and s =
        sqrt(sum((xi-mean(X))^2)/(n-1)) with r = the r-th moment, xi = values
        of variable X, n = number of cases]:

        g  : g1 (skewness) and g2 (kurtosis) as used in many textbooks
             (Joanes & Gill's "type 1" measure); g1 = m3/m2^(3/2) and g2 =
             m4/m2^2-3

        g3 : as type(g) without subtracting 3 from the kurtosis measure as
             used in Stata's summarize command

        G  : G1 (skewness) and G2 (kurtosis) as used in SAS and SPSS (Joanes
             & Gill's "type 2" measure); G1 = g1*sqrt(n*(n-1))/(n-2) and G2 =
             ((n+1)*g2+6)*(n-1)/((n-2)*(n-3)); this is the default

        G3 : as type(G) adding 3 to the kurtosis measure

        b  : b1 (skewness) and b2 (kurtosis) as used in MINITAB and BMDP
             (Joanes & Gill's "type 3" measure); b1 = m3/s^3 and b2 =
             m4/s^4-3

        b3 : as type(b) without subtracting 3 from the kurtosis measure

    allobs specifies use of the maximum possible number of observations for
        each variable. The default is to use only those observations for
        which all variables in varlist are not missing.

    by() specifies one or more variables defining distinct groups for which
        moment-based statistics should be calculated. by() is allowed only
        with a single varname. The choice between by: and by() is one of
        precisely what kind of output display is required. The display with
        by: is clearly structured by groups while that with by() is more
        compact. To show moments for several variables and several groups
        with a single call to moments2, the display with by: is essential.

    format() controls the display format of mean, standard deviation,
        skewness and kurtosis, as follows. Up to four numeric formats may be
        given. The first numeric format given controls the display of the
        mean; any second numeric format that of the standard deviation; any
        third numeric format that of the skewness, and any fourth numeric
        format that of the kurtosis. Formats not specified default to %9.3f.

    matname() specifies the name of a matrix in which to save the results of
        (the last set of) calculations. There will be 5 columns.  The columns
        will contain n, mean, standard deviation, skewness and kurtosis.

    tabdisp_options are options of tabdisp other than format().

    variablenames specifies that the variable names of varlist should be used
        in display. The default is to use variable labels to indicate a set
        of variables.


Examples

    . sysuse auto
    . moments2 price
    . moments2 price, t(G3)
    . moments2 price, t(g3)
    . moments2 price-foreign
    . moments2 price-foreign, format(%5.1f %5.1f)
    . bysort rep78: moments2 mpg


Saved results

    moments2 saves the following results (of the last variable/by-group) in
    r():

    Scalars   
      r(N)           number of observations
      r(sum_w)       sum of the weights
      r(mean)        mean
      r(Var)         variance
      r(sd)          standard deviation
      r(skewness)    skewness
      r(kurtosis)    kurtosis
      r(sum)         sum of variable
      r(min)         minimum
      r(max)         maximum
      r(p1)          1st percentile
      r(p5)          5th percentile
      r(p10)         10th percentile
      r(p25)         25th percentile
      r(p50)         50th percentile
      r(p75)         75th percentile
      r(p90)         90th percentile
      r(p95)         95th percentile
      r(p99)         99th percentile

    Macros    
      r(type)        type of skewness and kurtosis measure


References

    Joanes, D. N. & Gill, C. A. (1998). Comparing measures of sample skewness
        and kurtosis. The Statistician, 47, 183-189.


Acknowledgments

    moments2 (and this help file) leans heavily on Nicholas Cox's moments
    (see: click here). moments2 does nothing more than adding the
    type()-option and making "type 2" (i.e. type(G)) measures of skewness and
    kurtosis the default.


Author

    Dirk Enzmann, University of Hamburg, Germany
    dirk.enzmann@uni-hamburg.de


Also see