There are many other important measures of probability distance. Some of these are particularly connected with relative entropy. For example:
* The total-variation distance, . This is connected to the divergence through Pinskers inequality:  Pinskers inequality is vacuous for any distributions where , since the total variation distance is at most . For such distributions, an alternative bound can be used, due to Bretagnolle and Huber (see, also, Tsybakov): 
* The family of Rényi divergences generalize relative entropy. Depending on the value of a certain parameter, , various inequalities may be deduced.
Other notable measures of distance include the Hellinger distance, histogram intersection, Chi-squared statistic, quadratic form distance, match distance, Kolmogorov–Smirnov distance, and earth movers distance'.