Statistics · Statistical distributions
Chapter 1 · 3
The idea
The normal approximation to the Poisson distribution
When λ is large, a Poisson count is close to N(λ, λ): rescale λ to the whole interval, correct for continuity, standardise with √λ, and run the same steps backwards to find a threshold count or an unknown λ, or to test a rate over a long interval.
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Statistics · Statistical distributions
The normal approximation to the Poisson distribution
When λ is large, a Poisson count is close to N(λ, λ): rescale λ to the whole interval, correct for continuity, standardise with √λ, and run the same steps backwards to find a threshold count or an unknown λ, or to test a rate over a long interval.
Why it works
Too many terms to add
A seismometer on the side of a volcano records small tremors at random, at a mean rate of per day. The scientists plan a -day campaign. How likely is it that they record more than tremors?The number of tremors is , and exactly, : thirty-one Poisson terms, one for each count from to . Draw the distribution, though, and its shape is one you already know. The bars trace out a bell.
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