7 problems

Drton–Xiao's conjecture. Based on simulations, the distribution of $T_{\boldsymbol{w}}$ is $\operatorname{Cauchy}(0,1)$, the Cauchy distribution with center $0$ and scale $1$.

Let $(X_1,X_2)$ be the bivariate Marshall–Olkin exponential distribution generated by independent exponential shock times $Z_1,Z_2,Z_{12}$ with positive parameters…

Let $X$ and $Y$ be positively dependent random variables, meaning that $\operatorname{Cov}(g(X),h(Y))\geq 0$ for all increasing functions $g,h\in L^2$. Positive-dependence represen…

Let $U_1,\dots,U_n$ be standard uniform random variables whose dependence is described by a Gaussian copula with positive correlation coefficients, and let sub-uniformity denote th…

Let $U_1,\dots,U_n$ be random variables with a dependence structure given by an elliptical copula or an Archimedean copula, and let sub-uniformity denote the property that the gene…

Cai and Jin's conjecture. The estimator $\widehat{p}(\gamma)$ will remain consistent under certain forms of weakly correlated dependence among the test statistics. The conjecture c…

Let $(X_i)$ be the stationary process in the paper, let $d\geq 2$, and let $\delta_2(k)$ denote the physical dependence coefficients. Define … The paper's condition … can be weaken…