In this paper we investigate the combined effects of quantization and clipping on high-order function neural networks (HOFNN). Statistical models are used to analyze the effects of quantization in a digital implementation. We analyze the performance degradation caused as a function of the number of fixed-point and floating-point quantization bits under the assumption of different probability distributions for the quantized variables, and then compare the training performance between situations with and without weight clipping. We establish and analyze the relationships for a true nonlinear neuron between inputs and outputs bit resolution, training and quantization methods, network order and performance degradation, all based on statistical models, and for on-chip and off-chip training. Our experimental simulation results verify the presented theoretical analysis.