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G
gcurl10-Marble
10-Marble
April 24, 2017
Solved

graph curve manipulation

  • April 24, 2017
  • 5 replies
  • 19922 views

Hi All,

I am trying to get a skewed bell curve to represent a chemical in a reaction via an equation. This first bell curve will be subtracted from another skewed bell curve that represents a second chemical in the reaction. I have tried many equation types and have settled on the one that I am currently using. The trouble is that I cannot manipulate the equation variables enough to attain the configuration that is needed.

Would you all inspect my equation and advise me on whether it can be edited to fit the Benchmark dots on the graph. Maybe another variable can be inserted into the equation? If, not, can you recommend a new equation? The curve slopes are not as critically important as the start, finish, and peak positions and values.

As of now, the starting(blue) and finishing(cyan) points are good. It is the peak(green) that must move to the right without sacrificing the other positions.

All help is very appreciated.

Thank you,

Gary

Mathcad 11

Best answer by gcurl

Hi All,

I have been working very hard on finalizing this issue. I had posted a file earlier(weeks ago) that at that time was going to be the one. Since then I have taken a closer look at a file that Luc posted that back then wasn't close enough to what I needed. I have made his method work great for me. I found that I also needed the variability that his methodology affords. I can easily move the nodes around by changing the node's x,y values.

I might also insert a 'node' at the lower left of the curve which would allow me to vary the upward onset; similar to what I did at the end of the curve with the downward finish.

I appreciate everyone's contributions as they all allowed me to open my thought process.

After the Mods approve this post, I will mark it as "answered".

Thank you All,

Gary

5 replies

W
Werner_E25-Diamond I
25-Diamond I
April 24, 2017

Unfortunately you forgot to atatch your worksheet.

To be able to attach files you will first switch to "Advanced Editor" (upoer right corner of edit window) and then you ar offered the option "attach" at the lower right.

L
LucMeekes23-Emerald IV
23-Emerald IV
April 24, 2017

Without seeing the sheet, a distribution function that is often used to mimic many kinds of distributions is the Beta distribution.

In a more elaborate form than what Mathcad provides, it is:

Hope this helps.

Success!

Luc

G
gcurl10-MarbleAuthor
10-Marble
April 24, 2017

Thank you Werner Exinger and LucMeekes,

I did attach my file but somehow it did not get posted. I will now post it.

The dBeta function seems to not have the asymptotal style at both ends, but I will look at it.

Please have a look at the attached file and see if it can be changed to fit the benchmarks.

Thank you All,

Gary

L
LucMeekes23-Emerald IV
23-Emerald IV
April 24, 2017

Ah, with this kind of shape you will want to use the lognormal distribution. Why? Distribution Fitting - Chemical Yield Analysis

Use the dlnorm function. Here's an attempt:

You mention that you need asymptotes for the point t(i) and v(k). It would help if they're not exactly zero, but slightly positive.

Do you have more points along the curve?

Success!
Luc

G
gcurl10-MarbleAuthor
10-Marble
April 24, 2017

Hi LucMeekes,

The top benchmark is very close but the other two have been squeezed into the middle. Can the left side be pushed back 60 points and the right side be pushed ahead 120 points; to the benchmarks? I did have the ln function in the equation. Please pardon me for not being heavy into the statistical jargon, although I am somewhat familiar with it.

I see that I should also include needing an equation that I can adopt into php coding. I don't know if php will accept dlnorm language?

I just read up on lognormal distribution and it just so happens that I did choose that equation after much trial and error. So my equation is the lognormal distribution, albeit in an edited state and a longer version than dlnorm.

Thank you for the link. I read it, understand it, and appreciate it.

RE: In my previous Reply, the file posted as a zip for some reason.

Gary

G
gcurl10-MarbleAuthor
10-Marble
May 1, 2017

Hi All,

I acquired a different equation from a file that I received online entitled GUMBEL. I can't recall where I got it. I owe thanks to the unknown author of this file. I manipulated it and came up with a very close result. Here it is.

Thank you All for your assistance.

This should effectively close this thread.

Gary

L
LucMeekes23-Emerald IV
23-Emerald IV
May 1, 2017

So now, finally, you are providing more points!

G
gcurl10-MarbleAuthor
10-Marble
May 1, 2017

Hi Luc,

Ok, I provided 2 more benchmark points. I always stated that I didn't really care how the two slopes went as long as they were smooth. I still don't have an exact match for the slopes. All I ever really needed were the start, the peak, and the end; 3 benchmark points.

But, I should have relented when you asked for more so I apologize for not putting that out there. And, I thought that by only providing 3 benchmark points, that would free you up from being too restricted. I was caught between the proverbial angel and devil. I should have done it the way that you asked; I must have listened to the devil. I have learned for the next time.

Sincerely,

Gary

G
gcurl10-MarbleAuthorAnswer
10-Marble
May 31, 2017

Hi All,

I have been working very hard on finalizing this issue. I had posted a file earlier(weeks ago) that at that time was going to be the one. Since then I have taken a closer look at a file that Luc posted that back then wasn't close enough to what I needed. I have made his method work great for me. I found that I also needed the variability that his methodology affords. I can easily move the nodes around by changing the node's x,y values.

I might also insert a 'node' at the lower left of the curve which would allow me to vary the upward onset; similar to what I did at the end of the curve with the downward finish.

I appreciate everyone's contributions as they all allowed me to open my thought process.

After the Mods approve this post, I will mark it as "answered".

Thank you All,

Gary

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