Rate Parameter (Lambda)
Definition
The single parameter of the Poisson distribution, equal to both the mean and the variance of the distribution. In forensic contexts lambda is the expected number of events (e.g., particles, rare alleles) per unit of time, area, or volume.
- Symbol
- Lambda
- Distribution
- Poisson
- Equals
- Both the mean and the variance
- Forensic meaning
- Expected event count per unit time, area, or volume
Common questions
Why is it notable that lambda equals both the mean and the variance of the Poisson distribution?+
It is a defining property unique to the Poisson model, and it lets an analyst estimate the expected spread of counts directly from a single observed average rate, without needing a separate variance estimate, though it also means the model fits poorly when real data are more dispersed than that.
What kind of forensic count data is typically modelled with a Poisson rate parameter?+
Rare, discrete events counted over a fixed interval fit the model well, such as the number of matching rare alleles observed, particle counts in a defined volume of trace material, or incident counts over a time period, provided the events occur independently.
Related terms
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- Shape and Rate Parameters
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