### Two options for cFDR

My method of using non-bounded KDEs gives V values that never reach 1. Instead, we investigate using ecdfs. Integrating over ecdfs rather than KDEs extends the range of V values, meaning small V get smaller and V near to 1 get nearer to 1 (regardless of the annotation).

Our two options are:

Chrisâ€™ method: Convert Jamesâ€™ `vl()`

function to take a continuous q (this new function is called `vl2()`

) and integrate ecdf over these L curves. This method takes 32 mins for all 121,000 SNPs.

Combo method: Integrate ecdf over my L curves (convert q to \([0,1]\) range, use Jamesâ€™ `vl()`

function to find L curves, convert \(y\) co-ordinate of these back to \((-Inf, Inf)\) range). This method takes 29 mins for all 121,000 SNPs.

Chrisâ€™ method gives spikier L curves: