A mantissa is the fractional part of a base-10 logarithm after its integer characteristic has been separated. For log10(287,437) = 5.458543, the characteristic is 5 and the mantissa is 0.458543. section 12.5.4
In Benford analysis, mantissas should be uniformly distributed between 0 and 1 when leading digits follow Benford’s law. The overall distribution matters more than any single summary statistic. section 12.1 section 12.5.4
Compute and evaluate mantissas in a numeric data set:
- Calculate each value’s base-10 logarithm. section 12.5.4
- Subtract the integer part of the logarithm from the logarithm itself: mantissa = log10(value) − int(log10(value)). section 12.5.4
- Assess the distribution with its mean, variance, excess kurtosis, skewness, and rank-order plot. section 12.5.4
- Compare the observed distribution with the uniform pattern expected under Benford’s law. section 12.1 section 12.5.4
>>> populations['mantissa'] = \
populations['log'] - populations['log'].astype(int)
Shows the Python derivation of mantissas by subtracting each logarithm’s integer part. section 12.5.4
Population mantissas
For population data, derive log and mantissa columns, then inspect the resulting values. The observed mean is 0.5088, variance is 0.0880, excess kurtosis is −1.1779, and skewness is −0.1128; a rank plot shows a close-enough uniform distribution. section 12.5.4
