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replace a_i with b_i's on the left side of the inequality
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Anthony Quas
Anthony Quas
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Sorry for the long title. What I mean is that for two vectors (a_1,...,a_n) and (b_1,...,b_n) with the property $a_i,b_i \geq 0 $ and $ \sum a_i =\sum b_i =1$.

If $ -\sum a_ilog(a_i) > -\sum a_ilog(a_i) $$ -\sum a_ilog(a_i) > -\sum b_ilog(b_i) $ implies $\sum a_i^2 < \sum b_i^2$ or something similar?

Sorry for the long title. What I mean is that for two vectors (a_1,...,a_n) and (b_1,...,b_n) with the property $a_i,b_i \geq 0 $ and $ \sum a_i =\sum b_i =1$.

If $ -\sum a_ilog(a_i) > -\sum a_ilog(a_i) $ implies $\sum a_i^2 < \sum b_i^2$ or something similar?

Sorry for the long title. What I mean is that for two vectors (a_1,...,a_n) and (b_1,...,b_n) with the property $a_i,b_i \geq 0 $ and $ \sum a_i =\sum b_i =1$.

If $ -\sum a_ilog(a_i) > -\sum b_ilog(b_i) $ implies $\sum a_i^2 < \sum b_i^2$ or something similar?

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gstar2002
gstar2002
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Is there a relationship between Entropy of a fininte distrete probability distribution and the squre sum of the values of probability mass function of that distribution?

Sorry for the long title. What I mean is that for two vectors (a_1,...,a_n) and (b_1,...,b_n) with the property $a_i,b_i \geq 0 $ and $ \sum a_i =\sum b_i =1$.

If $ -\sum a_ilog(a_i) > -\sum a_ilog(a_i) $ implies $\sum a_i^2 < \sum b_i^2$ or something similar?