<p>I hope that someone more knowledgeable than me will answer this question, but this is what I understand it is happening.</p>
<p>The bootstrap method gives an estimate of the probability distribution of the period, given the data. If the probability distribution were a Gaussian centered on the true period, you would probably see a Gaussian.</p>
<p>But when estimating the period of a radial velocity signal, this is often not the case. By looking at a peridogram, you see that there are many peaks, corresponding to the true period, to its harmonics and to other artifacts. In some cases it may even happen that a spurious peak is higher than the true period peak.</p>
<p>This is exactly what happens with the bootstrap method. You sample your data differently and as a result you may get one of the spurious peaks as the higher one and incorrectly select it as the period. This explains the look of your histogram. In your case, the bootstrap samples are most likely to select 1.372094d as the period, but also have a good chance to select 1.372105d. The values in between instead have a very low probability of being selected as the period.</p>

CC BY-SA 4.0
2021-08-30T17:52:23.513Z
Thank you very much
Anna-Kat
CC BY-SA 4.0
2021-08-30T17:36:50.603Z
2021-08-30T17:36:50.603Z
Prallax
<p>I have data consisting of radial velocities and times (covering about 10 000 days). The radial velocity changes with a period. I tried to find out the period using Stellingwerf's method (it was successful), and then I applied the bootstrap method to determine the uncertainty. I obtained a histogram that is very different from the Gaussian curve. What could be the cause?</p>

CC BY-SA 4.0
2021-08-30T15:57:41.637Z
Hi Anna-Kat, I really appreciate that you are asking all these questions, but _I beg you_ to provide some more context. What are you working on? I can only guess from your previous questions that this is about some kind of light curve. Unless you explain exactly what you have done and how it has gone wrong (maybe a picture of the histogram :) I'm afraid that it might be difficult to help you. Thank you
Prallax
CC BY-SA 4.0
2021-08-30T16:03:44.147Z
I edited the question
Anna-Kat
CC BY-SA 4.0
2021-08-30T16:58:58.647Z
For how many days does your light curve cover? Ten days? Ten thousand? "I have data consisting of radial velocities and times" is not really saying anything.
uhoh
CC BY-SA 4.0
2021-08-30T17:02:59.293Z
About 10 000 days
Anna-Kat
CC BY-SA 4.0
2021-08-30T17:05:59.993Z
I'm not an expert, but are you sure it should come out gaussian? Why do you believe it should? Sorry if this is a stupid question
Prallax
CC BY-SA 4.0
2021-08-30T17:18:23.820Z
I do not think that the histogram is wrong, but I am finding the reason for the shape. Usually, these results give something similar to the Gaussian curve.
Anna-Kat
CC BY-SA 4.0
2021-08-31T12:27:46.503Z
Not an expert in the field, but I know from experience that the look of a histogram is very dependent on the choice of binning. For example the same data can look unimodal or bimodal depending on the number of bins. How did you choose yours? There are some formulas, like Sturges if you assume a normal distribution: k = log2(n) + 1, where k is the number of bins and n the number of data.
Jean-Marie Prival
<data-analysis><radial-velocity>
Why histogram does not look like the Gaussian curve?
Anna-Kat
# Why histogram does not look like the Gaussian curve?

(Asked by: username_0 on 2021-08-30)

I have data consisting of radial velocities and times (covering about 10 000 days). The radial velocity changes with a period. I tried to find out the period using Stellingwerf's method (it was successful), and then I applied the bootstrap method to determine the uncertainty. I obtained a histogram that is very different from the Gaussian curve. What could be the cause?

**Tags:** data-analysis, radial-velocity

> **Comments:**
> **username_1**: Hi username_0, I really appreciate that you are asking all these questions, but _I beg you_ to provide some more context. What are you working on? I can only guess from your previous questions that this is about some kind of light curve. Unless you explain exactly what you have done and how it has gone wrong (maybe a picture of the histogram :) I'm afraid that it might be difficult to help you. Thank you  
> **username_0**: I edited the question  
> **username_2**: For how many days does your light curve cover? Ten days? Ten thousand? "I have data consisting of radial velocities and times" is not really saying anything.  
> **username_0**: About 10 000 days  
> **username_1**: I'm not an expert, but are you sure it should come out gaussian? Why do you believe it should? Sorry if this is a stupid question  
> **username_0**: I do not think that the histogram is wrong, but I am finding the reason for the shape. Usually, these results give something similar to the Gaussian curve.  
> **username_3**: Not an expert in the field, but I know from experience that the look of a histogram is very dependent on the choice of binning. For example the same data can look unimodal or bimodal depending on the number of bins. How did you choose yours? There are some formulas, like Sturges if you assume a normal distribution: k = log2(n) + 1, where k is the number of bins and n the number of data.  

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## 1 answers

### Answer by username_1 on 2021-08-30. Score: 2 | Accepted answer

I hope that someone more knowledgeable than me will answer this question, but this is what I understand it is happening.

The bootstrap method gives an estimate of the probability distribution of the period, given the data. If the probability distribution were a Gaussian centered on the true period, you would probably see a Gaussian.

But when estimating the period of a radial velocity signal, this is often not the case. By looking at a peridogram, you see that there are many peaks, corresponding to the true period, to its harmonics and to other artifacts. In some cases it may even happen that a spurious peak is higher than the true period peak.

This is exactly what happens with the bootstrap method. You sample your data differently and as a result you may get one of the spurious peaks as the higher one and incorrectly select it as the period. This explains the look of your histogram. In your case, the bootstrap samples are most likely to select 1.372094d as the period, but also have a good chance to select 1.372105d. The values in between instead have a very low probability of being selected as the period.

> **Comments:**
> **username_0**: Thank you very much  

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