statsmodels.stats.rates.confint_poisson¶

statsmodels.stats.rates.confint_poisson(count, exposure, method=None, alpha=0.05)[source]¶

Confidence interval for a Poisson mean or rate

The function is vectorized for all methods except “midp-c”, which uses an iterative method to invert the hypothesis test function.

All current methods are central, that is the probability of each tail is smaller or equal to alpha / 2. The one-sided interval limits can be obtained by doubling alpha.

Parameters:¶

count : array_like¶: Observed count, number of events.
exposure : arrat_like¶: Currently this is total exposure time of the count variable. This will likely change.
method : str¶: Method to use for confidence interval This is required, there is currently no default method
alpha : float in (0, 1)¶: Significance level, nominal coverage of the confidence interval is 1 - alpha.

Returns:¶

tuple (low, upp)

Return type:¶

confidence limits.

Notes

Methods are mainly based on Barker (2002) [1] and Swift (2009) [3].

Available methods are:

“exact-c” central confidence interval based on gamma distribution
“score” : based on score test, uses variance under null value
“wald” : based on wald test, uses variance base on estimated rate.
“waldccv” : based on wald test with 0.5 count added to variance computation. This does not use continuity correction for the center of the confidence interval.
“midp-c” : based on midp correction of central exact confidence interval. this uses numerical inversion of the test function. not vectorized.
“jeffreys” : based on Jeffreys’ prior. computed using gamma distribution
“sqrt” : based on square root transformed counts
“sqrt-a” based on Anscombe square root transformation of counts + 3/8.
“sqrt-centcc” will likely be dropped. anscombe with continuity corrected center. (Similar to R survival cipoisson, but without the 3/8 right shift of the confidence interval).

sqrt-cent is the same as sqrt-a, using a different computation, will be deleted.

sqrt-v is a corrected square root method attributed to vandenbrouke, which might also be deleted.

Todo:

missing dispersion,
maybe split nobs and exposure (? needed in NB). Exposure could be used to standardize rate.
modified wald, switch method if count=0.