A new multivariate distribution with variant tail weights and its application in robust regression analysis.

In this paper, we propose a new kind of multivariate distribution by allowing different degrees of freedom for each univariate component. Compared with the classical multivariate distribution, it is more flexible in the model specification that can be used to deal with the variant amounts of tail weights on marginals in multivariate data modeling. In particular, it could include components following the multivariate normal distribution, and it contains the product of independent -distributions as a special case.

The Association Between Coffee Consumption and Metabolic Syndrome in Adults: A Systematic Review and Meta-Analysis.

Previous meta-analyses that found an inverse association between coffee consumption and metabolic syndrome pooled data from cross-sectional and longitudinal studies, which could lead to potentially misleading conclusions. Hence, this work aimed to reassess this association by analyzing data from the 2 types of studies separately and including recent studies. Online databases including PubMed, Scopus, Embase, The Cumulative Index to Nursing and Allied Health Literature (CINAHL) Plus, and Science Direct were searched for relevant studies published up to July 2020.

New expectation-maximization-type algorithms via stochastic representation for the analysis of truncated normal data with applications in biomedicine.

To analyze univariate truncated normal data, in this paper, we stochastically represent the normal random variable as a mixture of a truncated normal random variable and its complementary random variable. This stochastic representation is a new idea and it is the first time to appear in literature. According to this stochastic representation, we derive important distributional properties for the truncated normal distribution and develop two new expectation-maximization algorithms to calculate the maximum likelihood estimates of parameters of interest for Type I data (without and with covariates) and Type II/III data.

A new multivariate zero-adjusted Poisson model with applications to biomedicine.

Recently, although advances were made on modeling multivariate count data, existing models really has several limitations: (i) The multivariate Poisson log-normal model (Aitchison and Ho, 1989) cannot be used to fit multivariate count data with excess zero-vectors; (ii) The multivariate zero-inflated Poisson (ZIP) distribution (Li et al., 1999) cannot be used to model zero-truncated/deflated count data and it is difficult to apply to high-dimensional cases; (iii) The Type I multivariate zero-adjusted Poisson (ZAP) distribution (Tian et al., 2017) could only model multivariate count data with a special correlation structure for random components that are all positive or negative.

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process.

We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin.