Bornhuetter-Ferguson Formula Proof
Revision as of 13:59, 3 July 2020 by 66.248.200.4 (talk) (Created page with "Prove that the following 2 formulations of the reported Bornhuetter-Ferguson method are equivalent: : '''Formulation 1''': :* Ult<sub>r-BF</sub> = z x Ult<sub>r...")
Prove that the following 2 formulations of the reported Bornhuetter-Ferguson method are equivalent:
- Formulation 1:
- Ultr-BF = z x Ultr-Dev + (1 – z) x UltECR
- where z = %reported = 1/CDF
- Formulation 2:
- Ultr-BF = (reported claims) + (1 – 1/CDF) x UltECR
Starting with Formulation 1:
- Ultr-BF
- = z x Ultr-Dev + (1 – z) x UltECR
- = 1/CDF x (reported claims) x CDF + (1 – 1/CDF) x UltECR
- = (reported claims) + (1 – 1/CDF) x UltECR
And the last line is Formulation 2. Since these steps are reversible, we can conclude that Formulation 1 is equivalent to Formulation 2.
