Difference between revisions of "Bornhuetter-Ferguson Formula Proof"
Jump to navigation
Jump to search
(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...") |
|||
| (4 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
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> | ||
| − | + | '''Proof''': | |
| − | + | Starting with Formulation 1 and using the fact that Ult<sub>r-Dev</sub> = (reported claims) x CDF, we have: | |
| − | |||
| − | |||
| − | : | ||
| − | And the last line is Formulation 2. Since these steps are reversible, we can conclude that 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 and Formulation 2 are equivalent. | ||
Latest revision as of 14:05, 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
Proof:
Starting with Formulation 1 and using the fact that Ultr-Dev = (reported claims) x CDF, we have:
- 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 and Formulation 2 are equivalent.
