Expand documentation of dual increase frequency.

paper/paper.md

@@ -189,7 +189,7 @@ Figure @fig:hist reveals possible challenges with using a simple average in crop
 
 ![Interactive tool screenshot showing 2050 outcomes distribution as changes from $y_{expected}$, showing deltas and claims rates with climate change on the top and without further climate change (counterfactual) on bottom.](./img/hist.png "Interactive tool screenshot showing 2050 outcomes distribution. This graphic depicts changes from $y_{expected}$, showing deltas and claims rates with further climate change on the top and without climate change (counterfactual) on bottom."){#fig:hist}
 
-Indeed, {{ dualIncreasePercent2050 }} of neighborhoods seeing higher claims rates under SSP245 in the 2050 series also report overall multi-year average yields remaining unchanged or even increasing. In other words, yield volatility could allow a sharp elevation in loss probability without necessarily decreasing overall mean yields substantially enough to reduce claims rates through $y_{expected}$. These results highlight a need for future research into alternative FCIP policy formulations, such as using historic yield variance when establishing production histories and $y_{expected}$.
+Indeed, {{ dualIncreasePercent2050 }} of neighborhoods seeing higher claims rates under SSP245 in the 2050 series also report overall multi-year average yields remaining unchanged or even increasing^[This is "dual increase frequency" where $y_{expected}$ staying the same or increasing while $p_{l}$ also stays the same or increases. The 2050 series contains multiple years and we report on the average annual dual increase frequency across all years.]. In other words, yield volatility could allow a sharp elevation in loss probability without necessarily decreasing overall mean yields substantially enough to reduce claims rates through $y_{expected}$. These results highlight a need for future research into alternative FCIP policy formulations, such as using historic yield variance when establishing production histories and $y_{expected}$.
 
 ### Impact to insurers
 Plans where loss is calculated against averages of historic yields may fail to capture an increase in risk due to changing shapes of yield delta distributions [@fcic_common_2020]. This could allow elevated loss and insurer strain to hide behind the smoothing effect of mean yields. In other words, risk may increase at the insured unit scale in a way that is "invisible" to some current policy instruments.