Data processing is a challenging problem in space applications. The limited bandwidth available for communication between satellites and the ground and the increasing resolution of scientific instruments make it virtually impossible to transfer all the data recorded on board. Although various mitigation strategies were developed, large amounts of on-board data are still lost. This paper presents a Field Programmable Gate Array (FPGA)-based architecture which is able to perform on-board nonlinear analysis of data and compute probability distribution functions of fluctuations. We propose two implementations for our solution, which can be used for space applications and also other computational contexts. On a spacecraft, the logic resources of the FPGA will typically be shared by several designs running various digital signal processing algorithms. That is why each algorithm should be designed in variants, optimized for different criteria, so that the entire group of algorithms makes an efficient usage of the FPGA resources. The proposed solution focuses on two major optimization criteria, area and speed, such that the FPGA resources are efficiently used. Also, the power consumption is at least two orders of magnitude less in comparison with classical software implementations. The solution was tested with both synthetic and real data and shows excellent results paving the way towards an application that can be ported on a space-grade FPGA.