Standard deviation confidence interval

Let SSD the sample standard deviation computed with N residuals (r_i) from a regression with k free parameters, i.e.,

If those measurements come from a normal parent population with standard deviation SD, then the quantity

has a chi-square distribution with N-k degrees of freedom (e.g., Lu 1960). In this case, the confidence interval (CI) on SD at a confidence level of 100(1-a) per cent is given by

where Q is the quantile function of the chi-square distribution with N-k degrees of freedom.

An online python calculator to compute the SD confidence interval is available HERE


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