significance

gammapy.stats.significance(n_on, mu_bkg, method='lima', n_on_min=1)

Compute significance for an observed number of counts and known background.

The default method="lima" gives the significance estimate corresponding to equation (17) from the Li & Ma paper [1] in the limiting of known background $\mu_{bkg} = \alpha \times n_{off}$ with $\alpha \to 0$.

It is given by the following formula:

$$S_{lima} = \sqrt{2} \left[ n_{on} \log \left( \frac{n_{on}}{\mu_{bkg}} \right) - n_{on} + \mu_{bkg} \right] ^ {1/2}$$

For method="simple", the significance estimate is given by:

$$S_{simple} = (n_{on} - \mu_{bkg}) / \sqrt{\mu_{bkg}}$$

Parameters

n_onarray_like

Observed number of counts

mu_bkgarray_like

Known background level

method{“lima”, “simple”}

Method for significance estimation

n_on_minfloat

Minimum n_on (return NaN for smaller values)

Returns

significancendarray

Significance estimate

See also

excess, significance_on_off

References

1

Li and Ma, “Analysis methods for results in gamma-ray astronomy”, Link

Examples

>>>

>>> significance(n_on=10, mu_bkg=2, method='lima')
4.0235256
>>> significance(n_on=10, mu_bkg=2, method='simple')
5.65685425