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July 24, 2009 8:39 AM Subscribe
Is it possible to derive a math function based on the shape of the curve plotted (in x&y), along with additional requirements? I flunked calculus...
Dear MathMeFites,
I have a distribution of y values as a function of x. The plot of the function looks like a normal distribution curve, except it starts close to the mean and have a long tail in the end. The x values have a given range (1 to 90 or 120)...and the area of the curve has to fit a given value. Is it possible to build a function based on these requirements? I vaguely remember reading this topic while in pre-calculus, but can't figure out where to trace it back. Any hints and pointers are gladly appreciated.
Dear MathMeFites,
I have a distribution of y values as a function of x. The plot of the function looks like a normal distribution curve, except it starts close to the mean and have a long tail in the end. The x values have a given range (1 to 90 or 120)...and the area of the curve has to fit a given value. Is it possible to build a function based on these requirements? I vaguely remember reading this topic while in pre-calculus, but can't figure out where to trace it back. Any hints and pointers are gladly appreciated.
Basically, there are many, many different functions which can all have the same form within a given x range. Your goal is to pick a simple type of function -- say, a sum of sin curves -- and then find parameters so that your function closely matches the data. For certain types of function, there are algorithms which make this processes easy.
As mpls2 points out, this is called curve fitting.
Good luck!
posted by wyzewoman at 8:49 AM on July 24, 2009
As mpls2 points out, this is called curve fitting.
Good luck!
posted by wyzewoman at 8:49 AM on July 24, 2009
So your data looks something like this?
There are tons of distribution functions out there though - figuring out what other people are using for similar data is a good first step.
posted by Dr Dracator at 9:33 AM on July 24, 2009
There are tons of distribution functions out there though - figuring out what other people are using for similar data is a good first step.
posted by Dr Dracator at 9:33 AM on July 24, 2009
Polynomial Interpolation. I have vague memories of doing this stuff in a numerical computation class.
posted by chunking express at 10:03 AM on July 24, 2009
posted by chunking express at 10:03 AM on July 24, 2009
Oh, and I think using splines for interpolation is more accurate.
posted by chunking express at 10:05 AM on July 24, 2009
posted by chunking express at 10:05 AM on July 24, 2009
Response by poster: Thank you all, these should get me busy for the weekend. I guess it wasn't pre-calc after all :)
@caddis: Yes, Excel is my best friend now.
@chunking express: I think I will go over the curve fitting one before I can digest the Polynomial Interpolation, looks heavy.
@Dr Dracatar: It looks like Weibull, but I have slight variations (wider x range etc).
posted by aseno at 3:43 PM on July 24, 2009
@caddis: Yes, Excel is my best friend now.
@chunking express: I think I will go over the curve fitting one before I can digest the Polynomial Interpolation, looks heavy.
@Dr Dracatar: It looks like Weibull, but I have slight variations (wider x range etc).
posted by aseno at 3:43 PM on July 24, 2009
What you're doing isn't strictly interpolation, since you are also obeying the restriction that Int(f(x)) = c, where c is some constant.
You might want to look at the shape parameters for some of the more common statistical distributions and see if anything works for you.
posted by onalark at 11:46 AM on July 29, 2009
You might want to look at the shape parameters for some of the more common statistical distributions and see if anything works for you.
posted by onalark at 11:46 AM on July 29, 2009
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posted by mpls2 at 8:45 AM on July 24, 2009