This document provides proofs of the following: • The binomial distribution can be approximated with a Gaussian distribution at large values of N . • The arcsin square-root transform is the variance stabilising transform for the binomial distribution. • The Gaussian approximation for the binomial distribution is more accurate at smaller values of N after the variance stabilising transform has b...

Interpretations for the q-binomial coefficient evaluated at −q are discussed. A (q, t)-version is established, including an instance of a cyclic sieving phenomenon involving unitary spaces. 1. The q-binomial The q-binomial coefficient is defined for integers k and n, with 0 ≤ k ≤ n, and an indeterminate q by

In recent years, a number of results have been developed which connect information measures and estimation measures under various models, including, predominently, Gaussian and Poisson models. More recent results due to Taborda and Pérez-Cruz relate the relative entropy to certain mismatched estimation errors in the context of binomial and negative binomial models, where, unlike in the case of ...