5 problems

Let $\bbbeta=(\beta_1,\ldots,\beta_m)$ be the block-parameter vector for the block-beta random polytope $\mathcal{P}_{n,d}^{\bbbeta}$. Negative-parameter extension conjecture. The…

Dual degenerate insertion conjecture. For every real $p<\frac{4}{\gamma^2}$,

Let $\operatorname{Beta}(\alpha_1,\alpha_2)$ denote a Beta random variable with parameters $\alpha_1,\alpha_2>0$, and let $s\ge1$. A positive random variable is generalized gamma c…

Let $\bm{\beta}_{p,q}$ and $\bm{\beta}'_{p,q}$ denote the beta and beta prime distributions, respectively, and let $\bm{\gamma}_p$ denote the gamma distribution, with parameters in…

Let $n\geqslant2$ and $\textbf{Y}=(Y_1,Y_2,\ldots,Y_n)$ be a vector of i.i.d. random variables. Let $G_a$ denote a gamma random variable with parameter $a$, and let $B_{a,b}$ denot…