In this article we introduce a family of valuative invariants defined in terms the p-th moment expected vanishing order. These lie between $$\alpha $$ and $$\delta -invariants. They vary continuously big cone semi-continuously families. Most importantly, they give sufficient conditions for K-stability Fano varieties, which generalizes -criterions literature. are also related to $$d_p$$ -geometr...

P(X = z t) = w t > 0. How to learn parameters {(w t , z t)} k t=1 ? Relatively straightforward given iid sample.

We propose a method for optimal portfolio selection using a Bayesian framework that addresses two major shortcomings of the Markowitz approach: the ability to handle higher moments and estimation error. We employ the skew normal distribution which has many attractive features for modeling multivariate returns. Our results suggest that it is important to incorporate higher order moments in portf...

Though often not explicitly stated, the method of moments is one of the heavily used methods in queueing analysis. A typical, tagged customer is traced as it proceeds through the system and the components of its delay are individually analyzed. Using the moments of these components, moments of the sojourn and waiting times of an arbitrary customer can be derived. By this method, expected values...