Difference between revisions of "Bornhuetter-Ferguson Formula Proof"
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(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...") |
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Prove that the following 2 formulations of the reported Bornhuetter-Ferguson method are equivalent: | 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-Dev</sub> + (1 – z) x Ult<sub>ECR</sub> | |
| − | + | * where z = %reported = 1/CDF | |
| − | + | '''Formulation 2''': | |
* Ult<sub>r-BF</sub> = (reported claims) + (1 – 1/CDF) x Ult<sub>ECR</sub> | * Ult<sub>r-BF</sub> = (reported claims) + (1 – 1/CDF) x Ult<sub>ECR</sub> | ||
Starting with Formulation 1: | Starting with Formulation 1: | ||
| − | + | * Ult<sub>r-BF</sub> | |
| − | + | : = z x Ult<sub>r-Dev</sub> + (1 – z) x Ult<sub>ECR</sub> | |
| − | + | : = 1/CDF x (reported claims) x CDF + (1 – 1/CDF) x Ult<sub>ECR</sub> | |
| − | + | : = (reported claims) + (1 – 1/CDF) x Ult<sub>ECR</sub> | |
And the last line is Formulation 2. Since these steps are reversible, we can conclude that Formulation 1 is equivalent to Formulation 2. | And the last line is Formulation 2. Since these steps are reversible, we can conclude that Formulation 1 is equivalent to Formulation 2. | ||
Revision as of 14:00, 3 July 2020
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.
