def expected_zeros(pseudo_size, mu, alpha):
min_allowed_alpha=10**-4
max_allowed_prob_zero=0.99
if alpha < min_allowed_alpha:
prob_zero = max_allowed_prob_zero
else:
prob_zero = np.min([np.power(1.0+alpha*mu, -1.0/alpha), 0.99])
expected_zeros = int(pseudo_size*(prob_zero/(1-prob_zero)))
return expected_zeros
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