Histogram tests are a commonly used method for characterizing analogue to digital converters. However, different stimuli signals can be used in the histogram test. An overview of common input stimuli for the test is presented. Previous works have analysed the statistical properties of the resulting histograms for different stimuli signals, separately. In this paper, generally applicable results for asymptotically unbiased minimum variance estimator and Cramer-Rao lower bound are derived, irrespective of used input stimuli. Where available, the general expression is compared and found in accordance with signal-specific expressions.