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I need to find a distribution or a model to fit this data set in Mathematica

data3 = {{1, 1.3}, {2, 2.4}, {3, 3.8}, {4, 4.8}, {5, 5.6}, {6, 
6.3}, {7, 6.9}, {8, 7.3}, {9, 7.6}, {10, 7.8}, {15, 8.25}, {18, 
8.3}, {20, 8.1}, {22.5, 7.6}, {30, 6.2}, {40, 3.9}, {50, 
1.8}, {60, 0.7}};

the data is from a resonance circuit

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closed as off-topic by Henrik Schumacher, m_goldberg, MarcoB, bobthechemist, LLlAMnYP Dec 20 '18 at 16:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – Henrik Schumacher, m_goldberg, MarcoB, bobthechemist, LLlAMnYP
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 4
    $\begingroup$ What have you tried already? More information about the data would also be extremely useful. $\endgroup$ – Carl Lange Dec 12 '18 at 15:06
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    $\begingroup$ FindFormula is supposed to help you get started by suggesting some models, but I don's find the suggestions useful. Try with NonlinearModelFit[data3, a x/Exp[b x] + c x + d, {{a, 2}, {b, .1}, {c, 0}, d}, x] $\endgroup$ – Gustavo Delfino Dec 12 '18 at 15:53
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    $\begingroup$ What does the data represent? It's generally a bad idea to try to fit to data without having some prior knowledge of what physical process generates the data and what fit is likely to be correct. Otherwise, the only thing you have to go on is the error in the fit and gut feeling. You can always get a perfect fit with 18 data points using $a_1 x^{17} + a_2 x^{16} + a_3 x^{15} + ... + a_{17} x + a_{18}$. If there's really no further detail, then I suppose you just have to guess, and @GustavoDelfino 's guess seems as good as any. $\endgroup$ – MassDefect Dec 12 '18 at 17:10
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    $\begingroup$ Here is my standard comment about this: Are you fitting a regression curve that happens to have a similar shape as a probability distribution or does the data represent a sample from a random variable and the associated numbers (data3[[All,2]) are some sort of relative frequencies? If the latter, you need the actual counts rather than relative frequencies. Also, you seem to have "binned" the data and you need the raw data. In short, you should give a brief explanation as to how the data was collected and what it represents. $\endgroup$ – JimB Dec 12 '18 at 18:35
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    $\begingroup$ rami mahmoud, if you are the same person as Rami1234, I recommend that you merge your accounts, so that you have less difficulty editing your own questions. $\endgroup$ – bbgodfrey Dec 12 '18 at 19:54
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here is a distribution that is very close to your data

data = Rest[4.1 Table[PDF[BetaDistribution[1.7,3.5],k],{k,0,1,1/74}]]   

ListPlot@data     

enter image description here

here is the comparison between the two sets when selecting the same points

data = Table[{n, 
Rest[4.1 Table[
   PDF[BetaDistribution[1.7, 3.5], k], {k, 0, 1, 
    1/74}]][[n]]}, {n, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 18, 20,
 22, 30, 40, 50, 60}}]

data3 = {{1, 1.3}, {2, 2.4}, {3, 3.8}, {4, 4.8}, {5, 5.6}, {6, 
6.3}, {7, 6.9}, {8, 7.3}, {9, 7.6}, {10, 7.8}, {15, 8.25}, {18, 
8.3}, {20, 8.1}, {22.5, 7.6}, {30, 6.2}, {40, 3.9}, {50, 1.8}, {60,
0.7}}    

ListPlot[{data, data3}]     

enter image description here

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  • $\begingroup$ What estimation method did you use? If this turns out to be a regression problem rather than a fitting a distribution problem, then something like nlm = NonlinearModelFit[data3, a (x/100)^b (1 - (x/100))^c, {a, b, c}, x]; might be better. $\endgroup$ – JimB Dec 12 '18 at 21:45
  • $\begingroup$ This method is too complicated for me to explain in the comment section. But it returns better results than FindFormula and similar functions. $\endgroup$ – J42161217 Dec 12 '18 at 21:55

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