Create plot routine for extractor feets.extractors.ext_stetson.StetsonJ

[leliel12]

Create plot routine for extractor StetsonJ.

Path: feets.extractors.ext_stetson.py

Features

• StetsonJ

Extractor Documentation

These three features are based on the Welch/Stetson variability index I (Stetson, 1996) defined by the equation:

$$I = \sqrt{\frac{1}{n(n-1)}} \sum_{i=1}^n { (\frac{b_i-\hat{b}}{\sigma_{b,i}}) (\frac{v_i - \hat{v}}{\sigma_{v,i}})}$$

where :math:b_i and v_i are the apparent magnitudes obtained for the candidate star in two observations closely spaced in time on some occasion i, σ_b, i and σ_v, i are the standard errors of those magnitudes, b̂ and hat{v} are the weighted mean magnitudes in the two filters, and n is the number of observation pairs.

Since a given frame pair may include data from two filters which did not have equal numbers of observations overall, the "relative error" is calculated as follows:

$$\delta = \sqrt{\frac{n}{n-1}} \frac{v-\hat{v}}{\sigma_v}$$

allowing all residuals to be compared on an equal basis.

StetsonJ

Stetson J is a robust version of the variability index. It is calculated based on two simultaneous light curves of a same star and is defined as:

$$J = \sum_{k=1}^n sgn(P_k) \sqrt{|P_k|}$$

with P_k = δ_ikδ_jk

For a Gaussian magnitude distribution, J should take a value close to zero:

>>> fs = feets.FeatureSpace(only=['StetsonJ'])
>>> features, values = fs.extract(**lc_normal)
>>> dict(zip(features, values))
{'StetsonJ': 0.010765631555204736}

References

Warnings

The original FATS documentation says that the result of StetsonJ must be ~0 for gausian distribution but the result is ~-0.41