Skip to content

Commit

Permalink
Update index.md
Browse files Browse the repository at this point in the history
  • Loading branch information
Athanaseus authored Sep 16, 2020
1 parent 7e2c670 commit f3346a6
Showing 1 changed file with 0 additions and 36 deletions.
36 changes: 0 additions & 36 deletions docs/index.md
Original file line number Diff line number Diff line change
Expand Up @@ -30,39 +30,3 @@ residual image. - highest peak flux ($flux_{peak}$) and the rms flux
($flux_{local_rms}$) around the peak in the residual image. - highest
peak flux ($flux_{peak}$) and the rms flux ($flux_{grobal_rms}$) in the
residual image.

$$DR = \frac{flux_{peak}}{\left | {flux_{min}} \right | } (1)
DR = \frac{flux_{peak}}{\left | {flux_{local_rms}} \right | } (2)
DR = \frac{flux_{peak}}{\left | {flux_{global_rms}} \right | } (3)$$

Statistical moments of distribution
-----------------------------------

The mean and the variance provide information on the location (general
value of the residual flux) and variability (spread, dispersion) of a
set of numbers, and by doing so, provide some information on the
appearance of the distribution of residual flux in the residual image.
The mean and variance are calculated as follows respectively

$$MEAN = \frac{1}{n}\sum_{i=1}^{n}(x_{i}) (4)$$

and

$$VARIANCE = \frac{1}{n}\sum_{i=1}^{n}(x_{i} - \overline{x})^2 (5)$$

whereby

$$STD\_DEV = \sqrt{VARIANCE} (6)$$

The third and fourth moments are the skewness and kurtosis respectively.
The skewness is the measure of the symmetry of the shape and kurtosis is
a measure of the flatness or peakness of a distribution. This moments
are used to characterize the residual flux after performing calibration
and imaging, therefore for ungrouped data, the r-th moment is calculated
as follows:

$$m_r = \frac{1}{n}\sum_{i=1}^{n}(x_i - \overline{x})^r (7)$$

The coefficient of skewness, the 3-rd moment, is obtained by

$$SKEWNESS = \frac{m_3}{{m_2}^{\frac{3}{2}}} (8)$$

0 comments on commit f3346a6

Please sign in to comment.