3 problems

Let $B^*(r,p)$ be a Pascal random variable with positive integer parameter $r$ and $0<p\leq 1$, with … and expectation $E[B^*(r,p)]=r/p$. The Pascal distribution infimum conjecture…

Let $Y_1,\ldots,Y_n$ be the observations, let $\bar{Y}_n$ be their sample mean, and define the sample variance by … The function $g(\nu)$ is the efficient score function, up to the…

Let $M_0$ be the binomial random variable discussed in the preceding bound, and consider the final integral term in the upper bound of Theorem, both with and without approximating…