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.
Naturally the same formula can be used for positive variables other than income and for units of observation other than households.
The last definition shows that MLD is nonnegative, since
MLD has been called "the standard deviation of ln(x)",[1] (SDL) but this is not correct.
The SDL is and this is not equal to the MLD.
follows a log-normal distribution with mean and standard deviation of
The MLD is a special case of the generalized entropy index.
Specifically, the MLD is the generalized entropy index with α=0.