- #1
McCoy13
- 74
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I'm doing an analysis where I have a set of random variables with some known uncertainties (the uncertainties are different for each random variable). The random variable is roughly Gaussian distributed. I'd like to get a meaningful characteristic value and uncertainty for the whole set. I can imagine two ways of doing this:
1) Take the mean of the data, and propagate the uncertainties as [itex]\sigma=\frac{1}{N}\sqrt{\Sigma \sigma_{x_i^2}}[/itex]. However, the propagating the uncertainty this way doesn't take into account the spread in the data set, i.e. only the values of [itex]\sigma_{x_i}[/itex] matter, not the values of [itex]x_i[/itex], whether they are broadly or narrowly distributed. Therefore this [itex]\sigma[/itex] is not representative of the data.
2) Fit a Gaussian to the histogram of the data. This gives me a [itex]\sigma[/itex] that is characteristic of the spread. However, it does not propagate the uncertainties I already know about my random variable.
What I'd like to do is propagate my uncertainties through the Gaussian fit, but I don't know how to do this and haven't been able to find a method to do so.
1) Take the mean of the data, and propagate the uncertainties as [itex]\sigma=\frac{1}{N}\sqrt{\Sigma \sigma_{x_i^2}}[/itex]. However, the propagating the uncertainty this way doesn't take into account the spread in the data set, i.e. only the values of [itex]\sigma_{x_i}[/itex] matter, not the values of [itex]x_i[/itex], whether they are broadly or narrowly distributed. Therefore this [itex]\sigma[/itex] is not representative of the data.
2) Fit a Gaussian to the histogram of the data. This gives me a [itex]\sigma[/itex] that is characteristic of the spread. However, it does not propagate the uncertainties I already know about my random variable.
What I'd like to do is propagate my uncertainties through the Gaussian fit, but I don't know how to do this and haven't been able to find a method to do so.