I wrote it mainly because I thought it was important to show where the density is concave. But then I realised that the bound I derived is always larger than the mode (and zero when the mode is zero).
The main concern about concavity is exactly ensuring the distribution is (strongly) unimodal. So I'm unsure the result in \ref{eq:logconcavity} is useful.
I wrote it mainly because I thought it was important to show where the density is concave. But then I realised that the bound I derived is always larger than the mode (and zero when the mode is zero).
The main concern about concavity is exactly ensuring the distribution is (strongly) unimodal. So I'm unsure the result in \ref{eq:logconcavity} is useful.