### 1. Introduction

I now have two methods for performing functional cFDR:

Using interpolation (i.e.Â Jamesâ€™ method of interpolating to find L curves)

Using contours (i.e.Â defining L curves directly as the contours of the cfdr curves)

I compare the results when using these two methods. Note that the mehods only differ in the final step of defining the L curves (the cfdr/ccut values are the same).

I also include two test data points to the analysis representing p,q pairs which should give \(v\approx 1\).

Red: \((p=1, q=max(q[sub])=0.8107107)\) gives `ccut = 0.9986857`

. Here I set \(q\) equal to the biggest \(q\) value out of the SNPs I find \(v\)-values for, which incedently is the minimum \(q\) over all 121,000 SNPs.

Green: \((p=1, q=lims[4]=1.154623)\) gives `ccut = 1`

. Here I set \(q\) equal to the upper q limit for the KDE of the joint, which is set to be 10% higher than \(q[sub]\). Note that this is a lot higher than the biggest \(q\) in the whole dataset.

### 2. Results using interpolation