1.5 X²-distance: Let p, q be the densities of probability distributions P, Q with respect to measure μ (μ can be a countable measure). Then d_X2 (P,Q)

is defined as

Then 0

2 (P,Q) 1 and d2 is independent of the choice of the dominating measure. It is not a metric, because it is not symmetric in P, Q.
Distance d2 dates back to Pearson in the 1930s and has many applications in statistical inference. The following relations hold between d2 and other distances:

Transcribed Image Text:

dx(P,Q) = = LAX #(2),9(*)>0 (p(x)-q(x)) du(x) q(x) TEX:p(2),q(2)>0