Finding a,b,c for Gaussian Model: A Puzzling Task

In summary, to input into a gaussian model using a set of data points, you need to find the three constants a, b, and c. The gaussian model is centered at x=c and intersects at (0,a). If the data doesn't have a "0", you can still find it by evaluating the gaussian at the x's of the data and minimizing the function f(a, b, c) = (y1 - y(x1))^2 + (y2 - y(x2))^2 + ... where (x1, y1), (x2, y2), ... are the data points. A controls the height of the curve and b controls the spread.
  • #1
h00zah
16
0
If given a set of data points, how do I find a,b,c to input into a gaussian model?

y = a exp (-(x-c) / b)2

I know it's centered at x=c
Intersects at (0,a), but if the data doesn't have a "0", how do you find it?
Also, a controls the height, but in what way? and b controls the spread, but in what way?

Or do I have this completely wrong?

I figured at (0,a) it would be the max height because a controls height, but that means a=c because c=center where y is at its maximum height, so that doesn't make sense.
 
Last edited:
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  • #2
This could be an idea: given your gaussian y(x) which depends on the three (for the moment arbitrary) constants a, b and c, evaluate it at the x's of your data. Then calculate

f(a, b, c) = (y1 - y(x1))^2 + (y2 - y(x2))^2 + ...

where (x1, y1), (x2, y2), ... are you data points.
Finally, choose a, b and c in such a way to minimize f.
 

Related to Finding a,b,c for Gaussian Model: A Puzzling Task

1. What is the Gaussian Model?

The Gaussian Model, also known as the Normal Distribution, is a statistical model that describes a bell-shaped curve of data. It is used to represent a wide range of real-world phenomena, including natural phenomena and human behaviors.

2. Why is finding a,b,c for the Gaussian Model a puzzling task?

Finding the parameters a, b, and c for the Gaussian Model can be challenging because there is no one-size-fits-all solution. The values of a, b, and c can vary depending on the data being analyzed and the specific goals of the study. This can make the task puzzling and require careful consideration and experimentation.

3. What do the parameters a,b,c represent in the Gaussian Model?

The parameter a represents the height or amplitude of the curve, b represents the mean or center of the curve, and c represents the standard deviation or spread of the curve.

4. How is the Gaussian Model used in scientific research?

The Gaussian Model is commonly used in scientific research to analyze and interpret data. It allows researchers to make predictions, identify patterns and outliers, and make inferences about populations based on a sample of data.

5. Can the Gaussian Model be used for all types of data?

The Gaussian Model can be used for many types of data, but it works best for continuous data that follows a normal distribution. If the data is not normally distributed, other statistical models may be more appropriate.

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