statsmodels.stats.rates.tolerance_int_poisson(count, exposure, prob=0.95, exposure_new=1.0, method=None, alpha=0.05, alternative='two-sided')[source]

tolerance interval for a poisson observation


Observed count, number of events.


Currently this is total exposure time of the count variable.

probfloat in (0, 1)

Probability of poisson interval, often called “content”. With known parameters, each tail would have at most probability 1 - prob / 2 in the two-sided interval.


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 tolerance interval is a closed interval, that is both low and upp are in the interval.


verified against R package tolerance



Hahn, Gerald J., and William Q. Meeker. 1991. Statistical Intervals: A Guide for Practitioners. 1st ed. Wiley Series in Probability and Statistics. Wiley.


Hahn, Gerald J., and Ramesh Chandra. 1981. “Tolerance Intervals for Poisson and Binomial Variables.” Journal of Quality Technology 13 (2): 100–110.