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sci.Poisson-distribution Calculator
Calculates Poisson distribution probabilities P(X=k) = e^(−λ)λ^k/k! and cumulative CDF for rare events modelled with mean rate λ. Poisson distribution arises when events occur independently at a constant mean rate — calls per minute, radioactive decays, and insurance claims all follow Poisson statistics.
Inputs
Lambda
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
K Events
Count of items or occurrences.
Results
P(X=k) probability
Reference formula or conversion factor shown for context.
P(X≤k) cumulative CDF
The value at the specified point or condition.
P(X>k)
Reference formula or conversion factor shown for context.
mean = variance = λ
Standard deviation squared — average squared deviation from the mean. Essential for ANOVA, regression, and many statistical tests, though the squared units make it less intuitive directly.
P(X=k) = λᵏe^(-λ)/k!
Reference formula or conversion factor shown for context.
application
Recommended use case or application for this configuration or result.