<p>The data do not demonstrate that the eccentricity can practically cover the whole range from 0 to 1. You have no binaries with <span class="math-container">$0.0 &lt; e &lt; 0.2$</span> and no binaries with <span class="math-container">$0.64&lt;e&lt;1$</span>, so it seems to me that the CDF you have presented is a correct representation of the data as it exists.</p>
<p>You could of course extend the x-axis range to go from 0 to 1, by drawing a line at <span class="math-container">$y=0$</span> for <span class="math-container">$0\leq x&lt;0.2$</span> and a line at <span class="math-container">$y=1$</span> for <span class="math-container">$0.64 &lt; x \leq 1$</span>.</p>

CC BY-SA 4.0
2024-04-10T13:09:20.773Z
I understand, but in practice, it may exist. How would one extend the x-axis and adapt the CDF given that we have the CDF for the range [0.2 to 0.64]?


My general question is: if the observed range of a parameter is known to be smaller than its physical range, can the CDF of the observational data be extended to cover the entire physical range of the parameter?
RKerr
CC BY-SA 4.0
2024-04-10T12:56:29.030Z
2024-04-10T13:12:13.883Z
2024-04-10T13:12:13.883Z
ProfRob
<p>Consider the following observations regarding the eccentricities of stellar binaries (just an example):</p>
<p><span class="math-container">$$e = [0.3, 0.45, 0.2, 0.52, 0.64, 0.34]$$</span></p>
<p>We can calculate the cumulative distribution function (CDF) for this given range. However, it's important to note that eccentricities of stellar binaries can theoretically range from 0.0 to 1.0. How can we adjust the obtained CDF for the observational range to encompass the entire physical range?</p>
<p><a href="https://i.sstatic.net/B4xXt.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/B4xXt.png" alt="CDF for observational range" /></a></p>

CC BY-SA 4.0
2024-04-10T14:57:00.707Z
Are you asking how to extend the horizontal axes to include the values 0 and 1? The plotting programme of your choice should allow that easily by explicitly giving the desired range for the horizontal axis. Is it sensibly to do? Yes or no... depends on what you want to show
planetmaker
<observational-astronomy><binary-star>
Extend CDF to physical range
RKerr
# Extend CDF to physical range

(Asked by: username_0 on 2024-04-10)

Consider the following observations regarding the eccentricities of stellar binaries (just an example):

$$e = [0.3, 0.45, 0.2, 0.52, 0.64, 0.34]$$

We can calculate the cumulative distribution function (CDF) for this given range. However, it's important to note that eccentricities of stellar binaries can theoretically range from 0.0 to 1.0. How can we adjust the obtained CDF for the observational range to encompass the entire physical range?

[![CDF for observational range](https://i.sstatic.net/B4xXt.png)](https://i.sstatic.net/B4xXt.png)

**Tags:** observational-astronomy, binary-star

> **Comments:**
> **username_1**: Are you asking how to extend the horizontal axes to include the values 0 and 1? The plotting programme of your choice should allow that easily by explicitly giving the desired range for the horizontal axis. Is it sensibly to do? Yes or no... depends on what you want to show  

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## 1 answers

### Answer by username_2 on 2024-04-10. Score: 4 | Accepted answer

The data do not demonstrate that the eccentricity can practically cover the whole range from 0 to 1. You have no binaries with $0.0 < e < 0.2$ and no binaries with $0.64<e<1$, so it seems to me that the CDF you have presented is a correct representation of the data as it exists.

You could of course extend the x-axis range to go from 0 to 1, by drawing a line at $y=0$ for $0\leq x<0.2$ and a line at $y=1$ for $0.64 < x \leq 1$.

> **Comments:**
> **username_0**: I understand, but in practice, it may exist. How would one extend the x-axis and adapt the CDF given that we have the CDF for the range [0.2 to 0.64]?   My general question is: if the observed range of a parameter is known to be smaller than its physical range, can the CDF of the observational data be extended to cover the entire physical range of the parameter?  

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