Calculate the Gini coefficient of a 2D array.

The Gini coefficient is calculated using the prescription from Lotz et al. 2004 as:

\[G = \frac{1}{\left | \bar{x} \right | n (n - 1)} \sum^{n}_{i} (2i - n - 1) \left | x_i \right |\]

where \(\bar{x}\) is the mean over all pixel values \(x_i\).

The Gini coefficient is a way of measuring the inequality in a given set of values. In the context of galaxy morphology, it measures how the light of a galaxy image is distributed among its pixels. A Gini coefficient value of 0 corresponds to a galaxy image with the light evenly distributed over all pixels while a Gini coefficient value of 1 represents a galaxy image with all its light concentrated in just one pixel.

Usually Gini’s measurement needs some sort of preprocessing for defining the galaxy region in the image based on the quality of the input data. As there is not a general standard for doing this, this is left for the user.


The 2D data array or object that can be converted to an array.


The Gini coefficient of the input 2D array.