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So I have two probability distributions ,one from data and one from a model. They are not Gaussian shaped but skewed. I have measured their rms or width by finding the median and the 16% (lower limit) and 84% (upper limit) such that there is 68% of the area between these points. I defined the width as upper-lower/2.

But now I would like to say that the model does not match the data by X sigma, but how to say what X is. Each distribution has a sigma estimate (or distribution width) and each sigma estimate has an uncertainty derived from things with the model and data. So normally if only one sigma had an uncertainty I could say (sig1-sig2)/uncertainty but not sure how to combine them when each have uncertainties.

Another thing not sure about is since were dealing with variances should it be sig1^2-sig2^2/?

To possibly be more clear I have one distribution with measured width of 140+/-5 and one with 105+/- 12. So would I say I have an excess of (140-105)/sqrt(12^2+5^2)~2.75 or something like sqrt(140^2-105^2)/sqrt(12^2+5^2)~7.12 because in terms of saying I have a significant excess 2.75sigma and 7.12sigma are a lot different.

cinwick2321
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1 Answers1

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Answer:

You could always construct Confidence Interval for the Difference of Medians using Bootstrap methods. Bootstrap each sample separately, creating the sampling distribution for each median. Then calculate the difference between the two medians, and create the sampling distribution of those differences. Once we have that distribution we can establish a confidence interval.

I don't think, the way you describe the variances to be portrayed one in terms of other is statistically right. For skewed distribution, Bootstrapping method is well documented and you could apply it on the median and get the CI for the median. If I were you I will research into this.

Goodluck

Thanks

Satish

Satish Ramanathan
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