Average of power curve functions

AI Thread Summary
To find the average power curve function from the provided dataset, the mean of the coefficients and exponents can be calculated to create a representative function. The user aims to approximate the faulty motion reporting of a mouse sensor, which does not strictly follow a power curve but can be mimicked through available settings. The approach involves sampling data, approximating curves, and iterating to refine the average function. While a simple power curve is preferred for now, there are limitations on precision, suggesting that a higher-order polynomial may be necessary in the future. Ultimately, the goal is to achieve a reasonable approximation through this averaging process.
Labyrinth
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I have a program that generates a bunch of power curve functions and would like to know what the 'average' function between all of them would be.

Here is my data set so far:

4.638013x^0.076682586
4.834884x^0.034875062
4.0432342x^0.13476002
3.8535004x^0.12178477

How do I do this, and what is the average function for this particular set?

Thank you for your time.
 
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It depends on what you mean by 'average'.
 
I think the mean would be ideal.

I'm looking at it from a graph standpoint, where I want to find one curve that best represents them all.
 
I would lean toward taking the average of the four coefficients (the numbers in front of the power functions), and the average of the four exponents. That would certainly give you a function whose graph would be somewhere in the middle of the other four.
 
Is it really that simple? I guess I had delusions of complexity.

Anyways thanks for your help.
 
Labyrinth said:
Is it really that simple?

The un-simple task you have not done is to figure out precisely what you are trying to accomplish. What do you intend to use this "average" function for?
 
Stephen Tashi said:
The un-simple task you have not done is to figure out precisely what you are trying to accomplish. What do you intend to use this "average" function for?

I'm attempting to approximate the faulty motion reporting of a mouse sensor in terms of a power curve which it doesn't really follow but is available to mimic in settings available with many interfaces that support acceleration. The data I get is a bit noisy, so I take a sample, approximate its curve with a graphing program, take another sample, approximate that one, and so on. Over many iterations the 'average' function between them all should be a reasonable approximation.

There's a definite limit on the precision as long as only a simple power curve is available. It's more precisely described as a higher order polynomial. At a later date I may get into its exact description in these terms but for now a simple power curve takes priority.
 
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