6 problems

Representability conjecture. Every maxoid is representable as the conditional-independence structure of a positive discrete distribution.

Bar-Lev–Bshouty–Enis conjecture. The pair $\left(v,\left(0,\infty\right)\right)$ is a variance function for all $n\in\mathbb{N}$ if and only if $\operatorname{Re}(u_1)\leq 0$. The…

A one-parameter natural exponential family (NEF) has a variance function $v$ defined on its mean domain $U$. Consider a polynomial with a simple root at $0$ and a complex root…

Let $X$ have density … where $c>0$ is known and the parameter space is $\mathbb{R}\setminus\{0\}$. Pinelis's completeness conjecture. The statistic $X$ is complete. For the paramet…

The multivariate skew-$t$ distributions are obtained by using the skewing function … with finite $\nu>0$, where $\Pi$ is the c.d.f. of a Student variable with $\nu+k$ degrees of fr…

Let $KS_{m,n}$ denote the two-sample Kolmogorov–Smirnov statistic for sample sizes $m$ and $n$, and let the two-sample DKWM inequality mean the bound with constant $C=2$ and the co…