The study of shapes of probability distributions, whether discrete or continuous, is simplified by viewing them through the revealing composition of density with quantile function. Following normalization, the resulting probability density quantiles (pdQ s) carry essential information regarding shapes, which enables simple classification by asymmetry and tail weights.
The pdQ s are not only location-scale free, but densities of absolutely continuous distributions having the same support [0,1]. This allows for comparisons between them using metrics such as the Hellinger or Kullback-Leibler divergences. Empirical estimates for both discrete and continuous cases will be described. Asymmetry is measured in terms of distance from the symmetric class, and tail-weight is defined in terms of boundary derivatives. Finally, divergence from, and convergence to, uniformity will be illustrated.
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify the ACE contact person at the host institution (Darren Condon) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)