Absolute discounting

An alternative discounting method is absolute discounting,^14.15 in which a constant value $m$ is subtracted from each count. The effect of this is that the events with the lowest counts are discounted relatively more than those with higher counts. The discount coefficient is defined as

$$d_a = \frac{a-m}{a}$$ (14.16)

In order to discount the same amount of probability mass as the Good-Turing estimate, $m$ must be set to:

$$m = \frac{c_1}{\sum_{a=1}^{A}a\,.\,c_a}$$ (14.17)