The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Build foundational knowledge of data science with this introduction ...

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 ...

Nonparametric estimation of probability density functions, both marginal and joint densities, is a very useful tool in statistics. The kernel method is popular and applicable to dependent data, ...

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 ...