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from functools import partial
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

@partial(np.vectorize, otypes=["float64"] * 2)
def mm_stds(rng, n_draws, alpha, beta, k=500):
    draws = np.log(rng.gamma(shape=beta, scale=alpha, size=(k, n_draws)))
    grad = beta - np.exp(draws) / alpha
    draws_var = draws.var(-1)

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