Follow-up Comment #4, patch #8052 (project pspp):
The SPSS documentation doesn't mention any limits on the domain of the input.
http://publib.boulder.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Fidh_mean.htm
(it says the weights must be positive, but does not mention the values).
In the special case, where a value is zero. It can be shown algebraically that
the harmonic mean is also zero:
h = a.b / (a+b)
= a.0 / a
So I retract my previous statement. I think now that if the
sum-of-reciprocals method is used, there should be a special case when one or
more values are zero. But I still don't see why negative values should be
treated specially.
I cannot find in the academic literature any indication that harmonic means
are defined only for positive values.
This would also fit with the parallel resistor analogy (yes negative resistors
do exist - kindof - see Horowitz and Hill).
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