Editing Receiver operating characteristic (section)

==Detection error tradeoff graph==
[[File:Example of DET curves.png|thumb|Example DET graph]]
An alternative to the ROC curve is the [[detection error tradeoff]] (DET) graph, which plots the false negative rate (missed detections) vs. the false positive rate (false alarms) on non-linearly transformed x- and y-axes. The transformation function is the quantile function of the normal distribution, i.e., the inverse of the cumulative normal distribution. It is, in fact, the same transformation as zROC, below, except that the complement of the hit rate, the miss rate or false negative rate, is used. This alternative spends more graph area on the region of interest. Most of the ROC area is of little interest; one primarily cares about the region tight against the ''y''-axis and the top left corner – which, because of using miss rate instead of its complement, the hit rate, is the lower left corner in a DET plot. Furthermore, DET graphs have the useful property of linearity and a linear threshold behavior for normal distributions.<ref>{{Cite book|last1=Navratil|first1=J.|last2=Klusacek|first2=D.|title=2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07 |chapter=On Linear DETs |s2cid=18173315|date=2007-04-01|volume=4|pages=IV–229–IV–232|doi=10.1109/ICASSP.2007.367205|isbn=978-1-4244-0727-9}}</ref> The DET plot is used extensively in the [[automatic speaker recognition]] community, where the name DET was first used. The analysis of the ROC performance in graphs with this warping of the axes was used by psychologists in perception studies halfway through the 20th century,{{Citation needed|date=July 2019}} where this was dubbed "double probability paper".<ref>{{cite book |title=Observer Performance Methods for Diagnostic Imaging: Foundations, Modeling, and Applications with R-Based Examples |author=Dev P. Chakraborty |publisher=CRC Press |date=December 14, 2017 |isbn=9781351230711 
 |page=214 |url=https://books.google.com/books?id=MwZDDwAAQBAJ&q="double+probability+paper"&pg=PT214 |access-date=July 11, 2019}}</ref>