Mathstudent7
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- Joined
- Aug 17, 2020
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- 14
https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation#Other_distributions
"For non-normal distributions an approximate (up to O(n−1) terms) formula for the unbiased estimator of the standard deviation is: https://wikimedia.org/api/rest_v1/media/math/render/svg/7c03af4ff7000635c861b4e28f7cb99958148333
I would greatly appreciate if somebody can find any reference how this formula above using excess kurtosis is derived? There's lot information about how the correction factor for normal distrubuted populations is derived (n - 1.5): https://www.tandfonline.com/doi/abs/10.1080/00031305.1969.10481865
But how is the version for non-normal distributed populations, using excess kurtosis, derived?
"For non-normal distributions an approximate (up to O(n−1) terms) formula for the unbiased estimator of the standard deviation is: https://wikimedia.org/api/rest_v1/media/math/render/svg/7c03af4ff7000635c861b4e28f7cb99958148333
I would greatly appreciate if somebody can find any reference how this formula above using excess kurtosis is derived? There's lot information about how the correction factor for normal distrubuted populations is derived (n - 1.5): https://www.tandfonline.com/doi/abs/10.1080/00031305.1969.10481865
But how is the version for non-normal distributed populations, using excess kurtosis, derived?