Poisson distribution concept
| Definition | The distribution of a count of rare events, the limit of the binomial when n is large and p small with np held at mu, with mean and variance both mu. It is the null under which retrieval slots are handed out at random, and the Poisson ceiling is its tail. Primer S, equation S.7. Also Poisson. |
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| Example | With mean 0.1 the probability of a count of three or more is 0.000155, which times fifty thousand points is 7.7. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id poisson-distribution, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.7. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation S.7.
\[\Pr[X=k]=e^{-\mu}\frac{\mu^{k}}{k!},\qquad \mathbb E[X]=\operatorname{Var}(X)=\mu.\]
Conditions
none
Ledger
none
First stated
Primer S section S.3 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.
Measurements
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Failures and corrections
none
Invariance envelope
none declared
Machine checked
none
Used in
Data Mining as Observation primer S, chapters 0, 3, 5.
Related
Poisson ceiling; Bernoulli, binomial; null model; hub.
See also
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Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.