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[gnuastro-commits] master 83aae029: Book: corrected outputs in STD vs er
From: |
Mohammad Akhlaghi |
Subject: |
[gnuastro-commits] master 83aae029: Book: corrected outputs in STD vs error section |
Date: |
Sat, 3 Feb 2024 12:55:19 -0500 (EST) |
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:
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