1
$\begingroup$

I need to model my data ($(x,y)$ pairs) using the following exponential function:

$$f(x) = \exp((x + a)/b) - c$$

So, I need to find $a, b, c$ coefficients that are the best fit for my data. What is the algorithm that can solve this problem?

  • 2
    It depends on the probability model for the errors. Typically the observed value of $f(x)$ differs from the true $f(x)$; otherwise all the data points would fit the curve perfectly. You'd have a probability density $g(y)$ depending on $a$, $b$, $c$ and possible an error variance $\sigma^2$ or the like. Plug the data points into that function, and then view it as a function of $a,b,c,\sigma$. Find the values of $a,b,c,\sigma$ that maximize that function.2012-09-12
  • 0
    Are the $x$ values spaced equidistantly in the data? This is important for generalized Prony/Pisarenko methods.2016-08-19

2 Answers 2