What equation/distribution fits this data set?

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fenixtx423

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Joined
Dec 1, 2014
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This is a data set that I am trying to fit an equation to. The best I have come up with is two exponential curves added together or the Weibull distribution, but neither are a perfect fit. Any ideas?
x y
153.51
303.1135
42.42.8287
602.5502
84.82.1883
1201.8273
169.81.4503
2401.1108
339.40.79024
4800.54226
678.80.37759
9600.26832
1357.60.16609
19200.09051
2715.20.057455
38400.032173
 
Last edited:
On what basis are you concluding that any model must be an exact fit?
 
I am studying a natural phenomenon and across multiple data sets I have obtained this exact shape of curve (but scaled differently for each data set). You are correct, at this point I am just hoping that there is an equation that models this curve.
 
In general, you can't expect any theoretical distribution to fit a given data set perfectly. The best you can do is decide which distribution fits your data best, under whatever criterion you wish.
 
fenixtx423 said:
This is a data set that I am trying to fit an equation to. The best I have come up with is two exponential curves added together or the Weibull distribution, but neither are a perfect fit. Any ideas?
x y
153.51
303.1135
42.42.8287
602.5502
84.82.1883
1201.8273
169.81.4503
2401.1108
339.40.79024
4800.54226
678.80.37759
9600.26832
1357.60.16609
19200.09051
2715.20.057455
38400.032173
Click to expand...
Have you tried any regression like
u = ln(x)
v = ln(y)
v = a u2 + b u + c

EDIT: But that is (close to?) a Weibull, isn't it?
 
Last edited:
I have been able to obtain an almost perfect fit using the following function:

c1 * ( c2 / (c2 + X) )c3

where:
c1 = 3.92
c2 = 180.1
c3 = 1.5
 
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