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This paper is focused on the stochastic properties of quantization noise introduced by nonideal memoryless converters. In particular, overloading effects and integral nonlinearity (INL) are considered. A theoretical model is given, which accurately describes the quantization noise probability density function in presence of overloading noise and both deterministic and stochastic INL. A Gaussian stimulus is adopted for validation purposes due to its relevance in modern telecommunication systems. The proposed model is then used to derive quantization noise power as a function of both input signal and INL stochastic properties, in order to evaluate the average performance of classes of analog-to-digital converters (ADC). Finally, the results are applied to a memoryless converter affected by Gaussian INL, analyzing the properties of quantization noise.