[gnuastro-commits] master 83aae029: Book: corrected outputs in STD vs error section

[Mohammad Akhlaghi]

branch: master
commit 83aae029162a616118e3c93280084b87c9af0df7
Author: Elham <saremi_elham@yahoo.com>
Commit: Mohammad Akhlaghi <mohammad@akhlaghi.org>

    Book: corrected outputs in STD vs error section
    
    Until now, there was an ASCII histogram to show a normal distribution as an
    example in the Standard deviation vs error section. However, the reported
    statistics (values and histogram) from the commands (integers) did not
    match the floating point outputs in the book. This happened because this
    section was written before the Poisson distribution returned integers.
    
    With this commit, the output of statistics has been replaced to more
    precisely reflect the integer pixel statistics that the user sees after
    running the command.
---
 doc/gnuastro.texi | 42 ++++++++++++++++++++----------------------
 1 file changed, 20 insertions(+), 22 deletions(-)

diff --git a/doc/gnuastro.texi b/doc/gnuastro.texi
index ae484cd4..403affd1 100644
--- a/doc/gnuastro.texi
+++ b/doc/gnuastro.texi
@@ -29392,7 +29392,7 @@ Statistically speaking, a ``measurement'' is a sampling 
from an underlying distr
 Through our measurements, we aim to identify that underlying distribution (the 
``truth'')!
 With the command below, let's look at the pixel statistics of @file{1.fits} 
(output is shown immediately under it).
 
-@c If you change this output, replace the standard deviation (10.09) below
+@c If you change this output, replace the standard deviation (10.0) below
 @c in the text.
 @example
 $ aststatistics 1.fits
@@ -29401,26 +29401,24 @@ Statistics (GNU Astronomy Utilities) @value{VERSION}
 Input: 1.fits (hdu: 1)
 -------
   Number of elements:                      40000
-  Minimum:                                 -4.72824245470431e+01
-  Maximum:                                 4.24861780263050e+01
-  Mode:                                    0.09274776246
-  Mode quantile:                           0.5004125103
-  Median:                                  8.36190404450713e-02
-  Mean:                                    0.098637593
-  Standard deviation:                      10.09065298
+  Minimum:                                 61
+  Maximum:                                 155
+  Median:                                  100
+  Mean:                                    100.044925
+  Standard deviation:                      10.00066032
 -------
 Histogram:
- |                                  * ****
- |                                *********
- |                               ************
- |                              **************
- |                             *****************
- |                           ********************
- |                         ***********************
- |                        **************************
- |                      ******************************
- |                  **************************************
- |*    * *********************************************************** * *
+ |                          *  *
+ |                          *  *  *
+ |                       *  *  *  *
+ |                       *  *  *  *  *
+ |                       *  *  *  *  *
+ |                    *  * ********  * *
+ |                    *  ************* *
+ |                 *  ******************  *
+ |                 ************************  *
+ |              *********************************
+ |* ********************************************************** **      *
  |----------------------------------------------------------------------
 @end example
 
@@ -29496,10 +29494,10 @@ This is therefore defined as the @emph{standard error 
of the mean}, or ``error''
 From the example above, you see that the error is smaller than the standard 
deviation (smaller when you have a larger sample).
 In fact, @url{https://en.wikipedia.org/wiki/Standard_error#Derivation, it can 
be shown} that this ``error of the mean'' (@mymath{\sigma_{\bar{x}}}) is 
related to the distribution standard deviation (@mymath{\sigma}) through the 
following equation.
 Where @mymath{N} is the number of points used to measure the mean in one 
sample (@mymath{200\times200=40000} in this case).
-Note that the @mymath{10.09} below was reported as ``standard deviation'' in 
the first run of @code{aststatistics} on @file{1.fits} above):
+Note that the @mymath{10.0} below was reported as ``standard deviation'' in 
the first run of @code{aststatistics} on @file{1.fits} above):
 
-@c The 10.09 depends on the 'aststatistics 1.fits' command above.
-@dispmath{\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{N}} \quad\quad {\rm or} 
\quad\quad \widehat\sigma_{\bar{x}}\approx\frac{\sigma_x}{\sqrt{N}} = 
\frac{10.09}{200} = 0.05}
+@c The 10.0 depends on the 'aststatistics 1.fits' command above.
+@dispmath{\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{N}} \quad\quad {\rm or} 
\quad\quad \widehat\sigma_{\bar{x}}\approx\frac{\sigma_x}{\sqrt{N}} = 
\frac{10.0}{200} = 0.05}
 
 @noindent
 Taking the considerations above into account, we should clearly distinguish 
the following concepts when talking about the standard deviation or error: