@@ -20,6 +20,7 @@ title: "Table of Contents"
2020 &emsp ;&ensp ; 1.1.1. * [ Random variable] ( /D/rvar ) * <br >
2121 &emsp ;&ensp ; 1.1.2. * [ Random vector] ( /D/rvec ) * <br >
2222 &emsp ;&ensp ; 1.1.3. * [ Random matrix] ( /D/rmat ) * <br >
23+ &emsp ;&ensp ; 1.1.4. * [ Constant] ( /D/const ) * <br >
2324
2425 1.2. Probability <br >
2526 &emsp ;&ensp ; 1.2.1. * [ Probability] ( /D/prob ) * <br >
@@ -89,6 +90,7 @@ title: "Table of Contents"
8990 1.10. Further moments <br >
9091 &emsp ;&ensp ; 1.10.1. * [ Moment] ( /D/mom ) * <br >
9192 &emsp ;&ensp ; 1.10.2. ** [ Moment in terms of moment-generating function] ( /P/mom-mgf ) ** <br >
93+ &emsp ;&ensp ; 1.10.3. ** [ First central moment is zero] ( /P/momcent-1st ) ** <br >
9294
93952 . Information theory
9496
@@ -100,6 +102,8 @@ title: "Table of Contents"
100102 &emsp ;&ensp ; 2.1.5. * [ Joint entropy] ( /D/ent-joint ) * <br >
101103 &emsp ;&ensp ; 2.1.6. * [ Cross-entropy] ( /D/ent-cross ) * <br >
102104 &emsp ;&ensp ; 2.1.7. ** [ Convexity of cross-entropy] ( /P/entcross-conv ) ** <br >
105+ &emsp ;&ensp ; 2.1.8. ** [ Gibbs' inequality] ( /P/gibbs-ineq ) ** <br >
106+ &emsp ;&ensp ; 2.1.9. ** [ Log sum inequality] ( /P/logsum-ineq ) ** <br >
103107
104108 2.2. Differential entropy <br >
105109 &emsp ;&ensp ; 2.2.1. * [ Definition] ( /D/dent ) * <br >
@@ -122,13 +126,14 @@ title: "Table of Contents"
122126
123127 2.5. Kullback-Leibler divergence <br >
124128 &emsp ;&ensp ; 2.5.1. * [ Definition] ( /D/kl ) * <br >
125- &emsp ;&ensp ; 2.5.2. ** [ Non-negativity] ( /P/kl-nonneg ) ** <br >
126- &emsp ;&ensp ; 2.5.3. ** [ Non-symmetry] ( /P/kl-nonsymm ) ** <br >
127- &emsp ;&ensp ; 2.5.4. ** [ Convexity] ( /P/kl-conv ) ** <br >
128- &emsp ;&ensp ; 2.5.5. ** [ Additivity for independent distributions] ( /P/kl-add ) ** <br >
129- &emsp ;&ensp ; 2.5.6. ** [ Invariance under parameter transformation] ( /P/kl-inv ) ** <br >
130- &emsp ;&ensp ; 2.5.7. ** [ Relation to discrete entropy] ( /P/kl-ent ) ** <br >
131- &emsp ;&ensp ; 2.5.8. ** [ Relation to differential entropy] ( /P/kl-dent ) ** <br >
129+ &emsp ;&ensp ; 2.5.2. ** [ Non-negativity] ( /P/kl-nonneg ) ** (1) <br >
130+ &emsp ;&ensp ; 2.5.3. ** [ Non-negativity] ( /P/kl-nonneg2 ) ** (2) <br >
131+ &emsp ;&ensp ; 2.5.4. ** [ Non-symmetry] ( /P/kl-nonsymm ) ** <br >
132+ &emsp ;&ensp ; 2.5.5. ** [ Convexity] ( /P/kl-conv ) ** <br >
133+ &emsp ;&ensp ; 2.5.6. ** [ Additivity for independent distributions] ( /P/kl-add ) ** <br >
134+ &emsp ;&ensp ; 2.5.7. ** [ Invariance under parameter transformation] ( /P/kl-inv ) ** <br >
135+ &emsp ;&ensp ; 2.5.8. ** [ Relation to discrete entropy] ( /P/kl-ent ) ** <br >
136+ &emsp ;&ensp ; 2.5.9. ** [ Relation to differential entropy] ( /P/kl-dent ) ** <br >
132137
1331383 . Estimation theory
134139
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