Mean log deviation
In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. The MLD is zero when everyone has the same income, and takes larger positive values as incomes become more unequal, especially at the high end. Definition. The MLD of household income has been defined as where N is the number of households, formula_2 is the income of household "i", and formula_3 is the mean of formula_2. Naturally the same formula can be used for positive variables other than income and for units of observation other than households. Equivalent definitions are where formula_6  is the mean of ln("x"). The last definition shows that MLD is nonnegative, since formula_7 by Jensen's inequality. MLD has been called "the standard deviation of ln("x")", (SDL) but this is not correct. The SDL is and this is not equal to the MLD. For example, for the standard lognormal distribution, MLD = 1/2 but SDL = 1. Related statistics. The MLD is a special case of the generalized entropy index. Specifically, the MLD is the generalized entropy index with α=0.