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11-20-2015
08:53 AM

11-20-2015
08:53 AM

I want to approximate the experimental data by a curve as shown below on screenshot. I tried to use inverse probability density for the normal distribution, but without success. Are there any ideas in this regard (which equation can describe the data or maybe I need to create several sections/parts of the curve)?

Initial data:

The approximating curve must have the following form:

Or this form:

Solved! Go to Solution.

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11-21-2015
06:20 PM

11-21-2015
06:20 PM

Do you mean putting the Y data on a log10 scale?

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11-20-2015
09:55 AM

11-20-2015
09:55 AM

Re: Finding curve

Here's one possibility. The data has so much error you are unlikely to get a curve that looks like what you want though. The fitted parameters will be pretty much meaningless too.

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11-20-2015
10:18 AM

11-20-2015
10:18 AM

Re: Finding curve

See please Figs 12.9, 12.12 & 12.13 here

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11-21-2015
05:22 PM

11-21-2015
05:22 PM

Re: Finding curve

Richard,

Thank you. Whether and there are any ideas how to correct your model on a case of transition to a decimal logarithm?

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11-21-2015
06:20 PM

11-21-2015
06:20 PM

Do you mean putting the Y data on a log10 scale?

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11-21-2015
06:35 PM

11-21-2015
06:35 PM

Re: Finding curve

Thanks!

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11-22-2015
07:23 AM

11-22-2015
07:23 AM

Re: Finding curve

Richard,

Could you please explain what technique you used to set the approximating function and selection of the coefficients/constants in the equation?

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11-22-2015
08:27 AM

11-22-2015
08:27 AM

Re: Finding curve

I'm not sure what you mean. You started with dnorm, which has two parameters. One controls the shift along the x-axis (D1) and one controls the width (D2). It seemed clear to me that two more were needed to make the curve pass through the data: one to scale the y-axis and one to offset on the y-axis. So I added D3 and D4.

With the logarithmic y-scale I forced D2 to a positive value (using |D2|) because genfit was trying to make it negative, causing the fit to fail.

I chose the guess values by temporarily changing F(x):=f(x,D) to F(x):=f(x,guess) and adjusting the guess values until the curve roughly passed through the data. Then I changed it back.

Does that answer your question?

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11-23-2015
08:44 AM

11-23-2015
08:44 AM

Re: Finding curve

Ok. I see.

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11-20-2015
10:46 AM

11-20-2015
10:46 AM

Re: Finding curve

Does the term "shotgun pattern" apply? 😉

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11-21-2015
06:45 PM

11-21-2015
06:45 PM

Re: Finding curve

Absolutely .