Geometric mean for zero values

[#1]

One is sometimes precluded from using the geometric mean to descrtibe the location of data by the presence of zeros. SAS estimates the geometric mean as zero when there are zeros in the data. Here is a reasonable alternative:

/* A simple SQL implementation of a generalised geometric mean 
   for cases when the data contains some zeros. The GEOMEAN function from SAS
   returns zero if any of the data is zero. The generalised geometric
   mean is computed as a weighted average of zero and the geometric mean 
   of positive values. 

   This estimator was proposed by:
   Habib, Elsayed A. E. (2012) Geometric mean for negative and zero values. 
   IJRRAS 11 (3), p. 419-432.

   This implementation accounts for negative values by treating them as if
   they were zeros.
*/

title "Estimators of the geometric mean for the set {0, 1, 2, 3, 4}";

data test;
do x = 0 to 4;
    output;
    end;
run;

proc sql;
select 
    case when min(x) <= 0 then 0 else exp(mean(log(x))) end 
        as geoMean "Standard SAS geometric mean",
    exp(mean(log(x))) 
        as geoMeanPos "Geometric mean of positive values",
    exp(mean(log(x))) * count(log(x)) / count(x) 
        as geoMean0 "Weighted average geometric mean"
from test;
quit;

Standard SAS geometric mean	Geometric mean of positive values	Weighted average geometric mean
0	2.213364	1.770691