  We consider the non-parametric maximum likelihood estimation in the class of
Polya frequency functions of order two, viz. the densities with a concave
logarithm. This is a subclass of unimodal densities and fairly rich in general.
The NPMLE is shown to be the solution to a convex programming problem in the
Euclidean space and an algorithm is devised similar to the iterative convex
minorant algorithm by Jongbleod (1999). The estimator achieves Hellinger
consistency when the true density is a PFF_2 itself.
