We develop an estimation procedure for a discrete probability mass function (pmf) with unknown support. We derive its maximum likelihood estimator under the mild and natural shape-constraint of ...

A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates ...

Building on the widely-used double-lognormal approach by Bahra (1997), this paper presents a multi-lognormal approach with restrictions to extract risk-neutral probability density functions (RNPs) for ...