Exact CI for a Poisson Mean
Computes the exact confidence interval for the mean of a Poisson distribution, from an observed event count. It's the right tool for count data: number of defects per batch, accidents per month, particles detected per interval. The calculation uses the exact relationship between the Poisson and the chi-square distribution (Garwood's method), giving reliable bounds even when very few events were observed. Enter the number of events and the confidence level.
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Exact CI for a Poisson Mean
Computes the exact confidence interval for the mean of a Poisson distribution, from an observed event count. It's the right tool for count data: number of defects per batch, accidents per month, particles detected per interval. The calculation uses the exact relationship between the Poisson and the chi-square distribution (Garwood's method), giving reliable bounds even when very few events were observed. Enter the number of events and the confidence level.
How many events per interval, with a margin
Count data are everywhere: defects per batch, calls per hour, particles per sample, accidents per month. The Poisson distribution models this kind of phenomenon, and the practical question is: from an observed count, what is the plausible range for the true event rate? This exact confidence interval answers that.
The calculation exploits an elegant mathematical relationship between the Poisson and the chi-square distributions, known as Garwood's method. Instead of approximating the Poisson by a normal — which fails when there are few events — the bounds come directly from chi-square quantiles, with degrees of freedom derived from the observed count. This keeps the interval reliable even when only a handful of events, or none, were observed.
Enter the number of observed events and the confidence level. The tool returns the exact bounds for the Poisson mean. It's the correct option whenever the normal approximation would be risky because of a low count, a common situation with rare events, where uncertainty is greatest and deserves a rigorous method.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.