Why use the harmonic mean instead of a simple average?
The harmonic mean naturally handles the 2^(-M) probabilities that underpin the leading-zeros calculation, yielding an unbiased cardinality estimate. Simple averaging would produce systematic errors at very high cardinalities.
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Count Billions in 12 KilobytesHyperLogLog estimates cardinality by reading leading zeros in hashed values, trading 1% error for fixed memory.
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