Talk:Rényi entropy

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Why α=1 is special[edit]

Section doesn't feel like it's quite there yet. Maybe consider what happens when you're using a Renyi entropy as a measure of ecological diversity, and then realise that you need to split one species into two... -- Jheald 22:19, 23 January 2006 (UTC).

The first thing I saw was 1/(1-1) = inf Full Decent (talk) 16:07, 11 December 2009 (UTC)

To add[edit]

Renyi entropy was defined axiomatically in Renyi's Berkeley entropy paper. In this, a weakening of one of the Shannon axioms results in Renyi entropy; that's why α=1 is special. Also, some of Renyi entropy's applications - Statistical physics, General statistics, Machine learning, Signal processing, Cryptography (a measure of randomness, robustness), Shannon theory (generalizing, proving theorems), Source coding - should be added with context. I don't have all this handy right now, but I'm sure each piece of this is familiar to at least one person reading this page.... Calbaer 05:59, 5 May 2006 (UTC)

Also the continuous case is missing. -- Zz 11:58, 24 October 2006 (UTC)

non-decreasing?[edit]

The statement that H_\alpha is non-decreasing in \alpha seems to contradict the statement that H_\infty < H_2. Also, should that be a weak inequality? LachlanA 23:24, 21 November 2006 (UTC)

Mathworld says they're non-decreasing. I think that's an error; it probably depends on whether you're using positive or negative entropies. I've fixed the inequalities, an obvious example of H_\infty = H_2 = 2H_\infty is n=1, p_i = 1. ⇌Elektron 18:58, 29 June 2012 (UTC)