  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.
