Formulas for estimating average incomes by fractile
| P90–100=bi * P90 | |
| P95–100=bi * P95 | |
| P99–100=bi * P99 | |
| P99.5–100=bi * P99.5 | |
| P99.9–100=bi * P99.9 | |
| P99.99–100=bi * P99.99 | |
| P90–95=2 (P90–100) – (P95–100) | |
| P95–99=[ 5 (P95–100) – (P99–100) ] / 4 | |
| P99–99.5=2 (P99–100) – (P99.5–100) | |
| P99.5–99.9=[ 5 (P99.5–100) – (P99.9–100) ] / 4 | |
| P99.9–99.99=[ 10 (P99.9–100) – (P99.99–100) ] / 9 |
Source: Authors' analysis of state-level tax data from Sommeiller (2006) extended to 2011 using state-level data from the Internal Revenue Service SOI Tax Stats (various years), and Piketty and Saez (2012)