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This technique to find the sky value in a distribution was initially proposed in Akhlaghi and Ichikawa 201588.
Note that through the difference of the mode and median we have actually ‘detected’ data in the distribution. However this detection was only based on the total distribution of the data, not its spatial position in each mesh. So we adhere to the definition of Sky value in Sky value. Finding the median is very easy, the main problem is in finding the mode through a robust method. In Appendix C of Akhlaghi and Ichikawa (2015) a new approach to finding the mode in any astronomically relevant distribution is introduced.
Even when the mode and median are approximately equal, Cosmic rays can significantly bias the calculation of the average. Even if they are very few. However, usually, Cosmic rays have very sharp boundaries and do not fade away into the noise. Therefore, when the histogram of the distribution is plotted, they are clearly separate from the rest of the data. For example see Figure 15 in Akhlaghi and Ichikawa (2015). In such cases, \(\sigma\)-clipping is a perfect tool to remove the effect of such objects in the average and standard deviation. See Sigma clipping for a complete explanation. So after asserting that the mode and median are approximately equal in a mesh (see Tiling an image), convergence-based \(\sigma\)-clipping is also applied before getting the final sky value and its standard deviation for a mesh.
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GNU Astronomy Utilities 0.2.28-34fb manual, October 2016.