I have two vectors in R: an X vector and a Y vector. How do I do a Gaussian fit of the plot resulting from plotting Y vs. X using built-in functions? I ask this for multiple reasons. For one, I realized that a lot of languages/software such as MATLAB and R doesn't seem to have a built-in Gaussian fitter. This makes me wonder if there's an easy way to calculate it yourself. I don't know of any simple way, but I'm new to a lot of statistics.
The way I see it, there are two ways I can approach this. One is to take the mean of X and tweak the standard deviation until the sum of squared deviations are minimized (a la OLS regression). The other way is to interpret each pair (x_i, y_i) as an observation x_i and the frequency of observation y_i. Then I could use the formula for standard deviation to calculate it that way.
From what I can tell, these two methods don't necessarily bring about the same standard deviation. Which is correct, if either?