Quantile estimation by virtual probability method and application to waveform estimation with jitter noise

In this paper, a method to estimate quantiles of an unknown distribution without storing the collected data is proposed. By adding virtual samples according to the designed algorithm, the method transforms the problem of finding of quantile to the one of finding the median of a virtual distribution, such that the simple stochastic "Up and Down" model can be applied. Simulation results show good performance on the Gaussian distribution, especially at both the extreme ends of the quantiles. The application to signal estimation under jitter noise is demonstrated.