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

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  • Ruiz-Castro, Juan E.
  • Acal, Christian
  • Aguilera, Ana M.
  • Aguilera-Morillo, M. Carmen
  • Roldán, Juan B.

Abstract

Functional principal component analysis (FPCA) based on Karhunen–Loève (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.

Suggested Citation

  • Ruiz-Castro, Juan E. & Acal, Christian & Aguilera, Ana M. & Aguilera-Morillo, M. Carmen & Roldán, Juan B., 2021. "Linear-Phase-Type probability modelling of functional PCA with applications to resistive memories," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 71-79.
    • Handle: RePEc:eee:matcom:v:186:y:2021:i:c:p:71-79
    DOI: 10.1016/j.matcom.2020.07.006
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    References listed on IDEAS

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    1. Aguilera-Morillo, M. Carmen & Aguilera, Ana M. & Jiménez-Molinos, Francisco & Roldán, Juan B., 2019. "Stochastic modeling of Random Access Memories reset transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 197-209.
    2. Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    3. Juan Eloy Ruiz-Castro, 2018. "A D-MMAP to Model a Complex Multi-state System with Loss of Units," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel & Alex Karagrigoriou (ed.), Recent Advances in Multi-state Systems Reliability, pages 39-58, Springer.
    4. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.
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    Cited by:

    1. Christian Acal & Manuel Escabias & Ana M. Aguilera & Mariano J. Valderrama, 2021. "COVID-19 Data Imputation by Multiple Function-on-Function Principal Component Regression," Mathematics, MDPI, vol. 9(11), pages 1-23, May.

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