Replacing missing values with a value at the end of the distribution

Replacing missing values with a value at the end of the variable distribution is equivalent to replacing them with an arbitrary value, but instead of identifying the arbitrary values manually, these values are automatically selected as those at the very end of the variable distribution. The values that are used to replace missing information are estimated using the mean plus or minus three times the standard deviation if the variable is normally distributed, or the inter-quartile range (IQR) proximity rule otherwise. According to the IQR proximity rule, missing values will be replaced with the 75th quantile + (IQR * 1.5) at the right tail or by the 25th quantile - (IQR * 1.5) at the left tail. The IQR is given by the 75th quantile - the 25th quantile.