Fraction-of- Time Density Estimation Based on Linear Interpolation of Time Series

A new estimator for the probability density function of a signal observed over a finite observation interval is proposed. The estimator linearly interpolates adjacent samples and accommodates the presence of probability masses. The analysis is carried out in the fraction-of-time (FOT) probability framework where signals are modeled as single functions of time rather than sample paths of a stochastic process. Numerical results show the better performance of the proposed estimator with respect to the kernel-based estimator. Moreover, the usefulness of analyzing signals in the FOT framework is enlightened.