Distributional Data Analysis via Quantile Functions and Its Application to Modeling Digital Biomarkers of Gait in Alzheimer’s Disease Rahul Ghosal, Johns Hopkins Bloomberg School of Public Health; Vijay R. Varma, National Institute on Aging (NIA), National Institutes of Health (NIH); Dmitri Volfson, Neuroscience Analytics, Computational Biology, Takeda, Cambridge, MA, USA ; Inbar Hillel, Tel Aviv Sourasky Medical Center, Tel Aviv, Israel; Jacek Urbanek, Johns Hopkins University School of Medicine; Jeffrey M. Hausdorff, Tel Aviv University, Tel Aviv, Israel; Amber Watts, Department of Psychology, University of Kansas; Vadim Zipunnikov, Johns Hopkins Bloomberg School of Public Health