Shen, JieShen, YiWang, Ruodo2020-01-062020-01-062019-03https://doi.org/10.1016/j.spa.2018.03.023http://hdl.handle.net/10012/15404The final publication is available at Elsevier via https://doi.org/10.1016/j.spa.2018.03.023. © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that the set of all possible distributions of intrinsic location functionals for periodic stationary processes is the convex hull generated by a specific group of distributions. We then focus on two special subclasses of these random locations. For the first subclass, the density has a uniform lower bound; for the second subclass, the possible distributions are closely related to the concept of joint mixability.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalperiodic stationary processrandom locationjoint mixabilityArticle