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medpy.metric.histogram.chi_square

medpy.metric.histogram.chi_square(h1, h2)[source]

Chi-square distance.

Measure how unlikely it is that one distribution (histogram) was drawn from the other. The Chi-square distance between two histograms \(H\) and \(H'\) of size \(m\) is defined as:

\[d_{\chi^2}(H, H') = \sum_{m=1}^M \frac{ (H_m - H'_m)^2 }{ H_m + H'_m }\]

Attributes:

  • semimetric

Attributes for normalized histograms:

  • \(d(H, H')\in[0, 2]\)
  • \(d(H, H) = 0\)
  • \(d(H, H') = d(H', H)\)

Attributes for not-normalized histograms:

  • \(d(H, H')\in[0, \infty)\)
  • \(d(H, H) = 0\)
  • \(d(H, H') = d(H', H)\)

Attributes for not-equal histograms:

  • not applicable
Parameters:

h1 : sequence

The first histogram.

h2 : sequence

The second histogram.

Returns:

chi_square : float

Chi-square distance.