On 11 Aug 2003 at 15:31, Maarten Speekenbrink wrote: > Thank you Herman and Glen for your reply's...they have helped me a lot. > have read something on log-concave distributions and now believe that the > sum of log-concanve distributions will also have a log-concave distribution > (and therefore is unimodal). However, I am wondering why the distribution of > the sum of logistically distributed variables is clearly symmetric. Is the > distribution of a sum of symmetrically distributed variables always > symmetric?
That easy. X is symmetric about a iff (X-a) has the same distribution as -(X-a), and Y is symmetric about b iff (Y-b) has the same distribution as -(Y-b). A little algebra gives the result. Kjetil Halvorsen I will probably use the Chebyshev type inequality (is this the > Camp-Weidell inequality?) to compute a one-tailed probability bound, so I > think the information regarding symmetry is important. > > Thank you again for your help, and hopefully you can help me out here as > well! > > Regards, > > Maarten > > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
