statsmodels.stats.rates.confint_poisson¶
-
statsmodels.stats.rates.confint_poisson(count, exposure, method=
None
, alpha=0.05
, alternative='two-sided'
)[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.
- Parameters:¶
- countarray_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.
- alternative{“two-sider”, “larger”, “smaller”)
default: “two-sided” Specifies whether to calculate a two-sided or one-sided confidence interval.
- Returns:¶
- tuple (low, upp)
confidence
limits. When alternative is not “two-sided”, lower or upper bound is set to 0 or inf respectively.
- tuple (low, upp)
See also
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.
References
[1]Barker, Lawrence. 2002. “A Comparison of Nine Confidence Intervals for a Poisson Parameter When the Expected Number of Events Is ≤ 5.” The American Statistician 56 (2): 85–89. https://doi.org/10.1198/000313002317572736.
[2]Patil, VV, and HV Kulkarni. 2012. “Comparison of Confidence Intervals for the Poisson Mean: Some New Aspects.” REVSTAT–Statistical Journal 10(2): 211–27.
[3]Swift, Michael Bruce. 2009. “Comparison of Confidence Intervals for a Poisson Mean – Further Considerations.” Communications in Statistics - Theory and Methods 38 (5): 748–59. https://doi.org/10.1080/03610920802255856.