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Coupon Collector Problem for Non-Uniform Coupons: Bound on the number of missed Coupons

In fact I am interested in bounding $\mathbb E[G]$ incorporating an information theoretic measure on $\mathbf p$, e.g. the entropy of the distribution $\mathbf p$, the total variation distance of $\mathbf … overhang like ${\rm Pr}(\hat N \leq k) \geq \mathcal F(k,b,N,I(\mathbf p))$, as a function expression $\mathcal F$, which incorporate an information theoretic measure $\mathcal I(\mathbf p)$, e.g. the entropy
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