# Pirana 23.1.2 RSE for Omega & Sigma

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### #1 kengwah96

kengwah96

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Posted 16 August 2023 - 04:32 AM

Dear all,

I noticed in the Pirana 23.1.2 release updates, there is an update to the formula used for the calculation of RSE for sqrt(exp(OM^2) - 1) transformed Omega and Sigma.

Previous formula: RSE% = %RSEuntransformed/2

New formula: RSE% = exp(ParameterValue)/ (2*(exp(ParameterValue) – 1)) *ParameterValue*(%RSEuntransformed).

However, I am unable to find additional background information on the switch. Would appreciate it if someone could shed some light on this.

Many thanks.

Keng Wah

Edited by kengwah96, 16 August 2023 - 04:33 AM.

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### #2 kniefort

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Posted 17 August 2023 - 01:04 AM

Hi Keng,

The new formula is simply the correct one for calculating RSE% for that particular transform.  The previous formula was an approximation that lost accuracy as omega values increased.

The background would come from error propagation theory in statistics, i.e., see https://en.wikipedia..._of_uncertainty.

If you have further questions, please post and we can involve some of our mathematicians in the conversation!

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### #3 kengwah96

kengwah96

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Posted 18 August 2023 - 12:38 AM

Many thanks for the explanation!

Hi Keng,

The new formula is simply the correct one for calculating RSE% for that particular transform.  The previous formula was an approximation that lost accuracy as omega values increased.

The background would come from error propagation theory in statistics, i.e., see https://en.wikipedia..._of_uncertainty.

If you have further questions, please post and we can involve some of our mathematicians in the conversation!

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