hist.intervals module#
- hist.intervals.clopper_pearson_interval(num: ndarray[Any, dtype[Any]], denom: ndarray[Any, dtype[Any]], coverage: float | None = None) ndarray[Any, dtype[Any]] #
Compute the Clopper-Pearson coverage interval for a binomial distribution. c.f. http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
- Parameters:
num – Numerator or number of successes.
denom – Denominator or number of trials.
coverage – Central coverage interval. Default is one standard deviation, which is roughly
0.68
.
- Returns:
The Clopper-Pearson central coverage interval.
- hist.intervals.poisson_interval(values: ndarray[Any, dtype[Any]], variances: ndarray[Any, dtype[Any]] | None = None, coverage: float | None = None) ndarray[Any, dtype[Any]] #
The Frequentist coverage interval for Poisson-distributed observations.
What is calculated is the “Garwood” interval, c.f. V. Patil, H. Kulkarni (Revstat, 2012) or http://ms.mcmaster.ca/peter/s743/poissonalpha.html. If
variances
is supplied, the data is assumed to be weighted, and the unweighted count is approximated byvalues**2/variances
, which effectively scales the unweighted Poisson interval by the average weight. This may not be the optimal solution: see 10.1016/j.nima.2014.02.021 (arXiv:1309.1287) for a proper treatment.In cases where the value is zero, an upper limit is well-defined only in the case of unweighted data, so if
variances
is supplied, the upper limit for a zero value will be set toNaN
.- Parameters:
values – Sum of weights.
variances – Sum of weights squared.
coverage – Central coverage interval. Default is one standard deviation, which is roughly
0.68
.
- Returns:
The Poisson central coverage interval.
- hist.intervals.ratio_uncertainty(num: ndarray[Any, dtype[Any]], denom: ndarray[Any, dtype[Any]], uncertainty_type: Literal['poisson', 'poisson-ratio', 'efficiency'] = 'poisson') Any #
Calculate the uncertainties for the values of the ratio
num/denom
using the specified coverage interval approach.- Parameters:
num – Numerator or number of successes.
denom – Denominator or number of trials.
uncertainty_type –
Coverage interval type to use in the calculation of the uncertainties.
"poisson"
(default) implements the Garwood confidence interval for a Poisson-distributed numerator scaled by the denominator. Seehist.intervals.poisson_interval()
for further details."poisson-ratio"
implements a confidence interval for the rationum / denom
assuming it is an estimator of the ratio of the expected rates from two independent Poisson distributions. It over-covers to a similar degree as the Clopper-Pearson interval does for the Binomial efficiency parameter estimate."efficiency"
implements the Clopper-Pearson confidence interval for the rationum / denom
assuming it is an estimator of a Binomial efficiency parameter. This is only valid if the entries contributing tonum
are a strict subset of those contributing todenom
.
- Returns:
The uncertainties for the ratio.