Probabilistic Rounding and Sheppard's Correction
b'When rounded data are used in place of the true values to compute the variance of a variable or a regression line, the results will be distorted. Under suitable smoothness conditions on the distribution of the variable(s) involved, this bias, however, can be corrected with very high precision by using the well-known Sheppard\\u2019s correction. In this paper, Sheppard\\u2019s correction is generalized to cover more general forms of rounding procedures than just simple rounding, viz., probabilistic rounding, which includes asymmetric rounding and\\nmixture rounding.'