A Nonparametric Cumulative Distribution Function Estimation and Random Number Generator Circuit

Statistical computing operations such as Bayesian inference, stochastic programming, image and signal processing and cryptography are based on estimating the density functions. The nonparametric density function estimation relaxes constraints on the distribution forms of random data/event, therefore enabling generic statistical methods that can handle arbitrary random distributions. The current mainstream approach is by implementing it algorithmically on general purpose machines (such as microcontrollers or CPUs), which limits its energy efficiency and scalability and is unsuitable for low power/area platforms (such as sensor nodes, IoT). This work proposes the increase of energy efficiency and scalability with the use of dedicated computing units for basic computing operations. CMOS-based mixed-signal circuits (accelerators) are designed for two fundamental computational operations in nonparametric statistics- (I) Estimation and storage of nonparametric cumulative density function (CDF) and (II) Nonparametric (non-uniform) random generation. To the best of our knowledge, this is the first work supporting a physical implementation of nonparametric statistics through CMOS-based circuits, and it is the first work proposing a CMOS-based nonparametric (non-uniform) random number generator. Kernel density method is employed for CDF estimation also; an inverse method is developed to generate random numbers based on estimated CDF. Analog and mixed-signal circuits are developed to support the estimation and storage of CDF and random number generation. Cadence simulation results with 45nm transistor model files are presented to validate the functionality of the system.