I am writing my thesis for the default probability estimation in low default portfolios. One way to estimate the probability of default is from the Cumulative Accuracy Profile (CAP) curve (Marco Van der Burgt 2007/2008 Calibrating Low-default Portfolios, using the Cumulative Accuracy Profile Journal of Risk Model Validation, Vol. 1, No. 4).
Is there any easy way to calculate the concavity k of the curve? I know that there is a package in R (LDPD, Surzhko 2015) but I cannot understand exactly how it works.