New easy to compute formulas for the moments of random variables appearing in the coupon collectorproblem

• Autorzy: León-García, Amaryani , Pérez, Aroldo , Bolívar-Cimé, Addy
• Języki publikacji: EN

Abstrakty

EN

Assuming that there are N types of coupons, where the prob- ability that the ith coupon appears is pi ≥ 0 for i = 1, . . . , N , with [formula], we consider the variable T^k which represents the number of acquisitions needed to obtain k ≤ N different coupons, and the variable Yn which represents the number of different coupons obtained in n acquisitions. In the coupon collector problem it is of interest to obtain the expected value of these random variables, as well as their rth moments. We provide new expressions for the rth moments of T_kand Y_n, and we give expressions for their moment generating functions. Unlike known formulas, our formula for the rth moment of T_k is given in terms of recursive expressions and that of Y_n is given in terms of finite sums, so that they can be easily implemented computationally. Furthermore, our formulas allow obtaining simplified expressions of the first few moments of the variables.

Słowa kluczowe

EN

coupon collector problem; combinatorial probability; moments; moment generating function

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2023
• Tom: Vol. 43, Fasc. 2
• Strony: 155--164
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

León-García, Amaryani

• División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, CP. 86690, Cunduacán, Tabasco, Mexico,

autor

Pérez, Aroldo

• División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, CP. 86690, Cunduacán, Tabasco, Mexico
• [e-mail]

autor

Bolívar-Cimé, Addy

• División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, CP. 86690, Cunduacán, Tabasco, Mexico,

Bibliografia

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Identyfikatory

DOI

10.37190/0208-4147.00130