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math.PR2026
Two Multi--Draw Coupon Collector models with different retention rules
Aristides V. Doumas, S. Spektor
In this paper we study two variants of the generalized coupon collector's problem, where our collector receives at each run d distinct coupons and keeps all the new observed coupon…
math.PR2026
Equal probabilities maximize the expected deficit in the siblings of the coupon collector
Aristides V. Doumas, S. Spektor
In the siblings (or brotherhood) variant of the coupon collector's problem, a main collector draws coupons until her own album is complete and passes every duplicate down a chain o…
math.PR2026
An inequality involving alternating binomial sums
Aristides V. Doumas
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically dis…