statsmodels.stats.rates.confint_quantile_poisson(count, exposure, prob, exposure_new=1.0, method=None, alpha=0.05, alternative='two-sided')[source]

confidence interval for quantile of poisson random variable


Observed count, number of events.


Currently this is total exposure time of the count variable.

probfloat in (0, 1)

Probability for the quantile, e.g. 0.95 to get the upper 95% quantile. With known mean mu, the quantile would be poisson.ppf(prob, mu).


Exposure of the new or predicted observation.


Method to used for confidence interval of the estimate of the poisson rate, used in confint_poisson. This is required, there is currently no default method.

alphafloat in (0, 1)

Significance level for the confidence interval of the estimate of the Poisson rate. Nominal coverage of the confidence interval is 1 - alpha.

alternative{“two-sider”, “larger”, “smaller”)

The tolerance interval can be two-sided or one-sided. Alternative “larger” provides the upper bound of the confidence interval, larger counts are outside the interval.

tuple (low, upp) of limits of tolerance interval.
The confidence interval is a closed interval, that is both low and
upp are in the interval.


Hahn, Gerald J, and William Q Meeker. 2010. Statistical Intervals: A Guide for Practitioners.