Functional principal component analysis based on Karhunen Loeve 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 KL 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.

翻译：基于Karhunen-Loève展开的函数主成分分析能够描述与多个系统和设备相关的主要特征的随机演化过程。识别主成分得分的概率分布对于表征整个流程至关重要。本研究旨在考虑一组能够精确拟合先前变换的统计分布族。为此，本文引入一类新的分布——线性相位型分布——用于对主成分进行建模。通过深入研究此类分布，并借助KL展开证明，在任意时间点对过程进行特定线性变换后所得结果服从相位型分布。由此，该过程的一维分布均属于同一线性相位型分布族。最后，本文开发并阐述了该模型在电阻式存储器复位过程中的应用实例。