5 problems

Chen–Rubin's conjecture. The sequence $m(n)-n$ decreases for integers $n\geq 1$.

Consider independent observations from the gamma distribution with shape parameter $\theta>0$ and scale $\beta=1$, and let $T=\overline{\ln(X)}$ be sufficient. Define the fiducial…

Gamma-difference median conjecture. The function $\alpha\mapsto\operatorname{Med}(Z_\alpha)$ is non-increasing for $\alpha\in(2,\infty)$. The source notes that, if the preceding co…

Gamma-sum median conjecture. The function $\alpha\mapsto\operatorname{Med}(Z_\alpha)$ is non-decreasing for $\alpha\in(0,1)$. This is one of two conjectures concerning medians of s…

Let $r>0$ and $\lambda>0$ be the shape and rate parameters of the Gamma distribution, and let $f_h$ be the solution of the Gamma Stein equation for a test function $h$ with bounded…