Linear-Phase-Type probability modelling of functional PCA with applications to resistive memories

[EN] Functional principal component analysis (FPCA) based on Karhunen-Loeve (K-L) expansion allows to describe the stochastic evolution of the main characteristics associated to multiple systems and devices. Identifying the probability distribution of the principal component scores is fundamental to characterize the whole process. The aim of this work is to consider a family of statistical distributions that could be accurately adjusted to a previous transformation. Then, a new class of distributions, the linear-phase-type, is introduced to model the principal components. This class is studied in detail in order to prove, through the K-L expansion, that certain linear transformations of the process at each time point are phase-type distributed. This way, the one-dimensional distributions of the process are in the same linear-phase-type class. Finally, an application to model the reset process associated with resistive memories is developed and explained. (C) 2020 Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS). ; We would like to thank F. Campabadal and M.B. Gonzalez from the IMB-CNM (CSIC) in Barcelona for fabricating and providing the experimental measurements of the devices employed here. We acknowledge the support of the Spanish Ministry of Science, Innovation and Universities under projects TEC2017-84321-C4-3-R, MTM201788708-P, IJCI-2017-34038 (also supported by the FEDER, Spain program) and the PhD grant, Spain (FPU18/01779) awarded to Christian Acal. This work has made use of the Spanish ICTS Network MICRONANOFABS ; Ruiz-Castro, JE.; Acal, C.; Aguilera, AM.; Aguilera-Morillo, MC.; Roldán, JB. (2021). Linear-Phase-Type probability modelling of functional PCA with applications to resistive memories. Mathematics and Computers in Simulation. 186:71-79. https://doi.org/10.1016/j.matcom.2020.07.006 ; 71 ; 79 ; 186