“…For the interested reader, local approximations akin to Lemma 3.1 were derived for the Poisson, binomial, negative binomial, multinomial, Dirichlet, Wishart and multivariate hypergeometric distributions in (Ouimet, 2021a, Lemma 2.1), (Ouimet, 2022a, Lemma 3.1), (Ouimet, 2021c, Lemma 2.1), (Ouimet, 2021b, Theorem 2.1), (Ouimet, 2022b, Theorem 1), (Ouimet, 2022d, Theorem 1), (Ouimet, 2022c, Theorem 1), respectively. See also earlier references such as Govindarajulu (1965) (based on Fourier analysis results from Esseen (1945)) for the Poisson, binomial and negative binomial distributions, and Cressie (1978) for the binomial distribution.…”