# KLDIV Kullback-Leibler or Jensen-Shannon divergence between two distributions

let consider following probability distributions

X   P                Q           Kullback                      Kullback_divergence
1   0.526810511     0.6557  -0.166341349                        11.97922287
2   0.213080233     0.0357  0.54919316
3   0.02600177     0.8491   -0.130769473
4   0.088595233     0.934   -0.301057372
5   0.546739097    0.6787   -0.170539661
6   0.28479873     0.7577   -0.40204582
7   0.082491531     0.7431  -0.261600315
8   0.106326487   0.3922    -0.200222185
9   0.92608417    0.6555    0.461696987
10  0.866939299   0.1712    2.028853203
11  0.122989593     0.706   -0.310072991
12  0.782494583   0.0318    3.615893457
13  0.030182806     0.2769  -0.09651152
14  0.580645161   0.0462    2.120337307
15  0.632129887     0.0971  1.708443428
16  0.118564409     0.8235  -0.331517665
17  0.98791467     0.6948   0.501651889
18  0.139591662     0.3171  -0.165238155
19  0.668691061   0.9502    -0.338953731
20  0.839289529   0.0344    3.868023675


i would like to know what this number shows us?does this express information about second distribution?or what is distance between two distribution,as i know if it far from $1$,then it means that they are really different,but which is good and real?please i need your advice's

• I do not see any probability distributions here. It would appear that "X" is a column indexing 20 distinct outcomes and that "P" and "Q" are supposed to be probabilities, but they cannot be, since they each sum to far more than $1$.
– whuber
Jul 9, 2014 at 14:51
• anyway forget about if sum exceed $1$,i am interested about method itself,then can be numbers even more then 10000 in value :D Jul 9, 2014 at 17:56
• yes $p(x)*ln(p(x)/q(x)$ Jul 9, 2014 at 17:51
• how if i got some value $k$,then what does it mean? Jul 9, 2014 at 17:53