Let G be a graph with no isolated vertices. A k-coupon coloring of G is an assignment of colors from [k] := {1, 2, . . . , k} to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [k]. The maximum k for which a k-coupon coloring exists is called the coupon coloring number of G, and is denoted χc(G). In this paper, we prove that every d-regular...

We study in this paper a generalized coupon collector problem, which consists in analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distrib...

Some new exact distributions on coupon collector’s waiting time problems are given based on a generalized Pólya urn sampling. In particular, usual Pólya urn sampling generates an exchangeable random sequence. In this case, an alternative derivation of the distribution is also obtained from de Finetti’s theorem. In coupon collector’s waiting time problems with m kinds of coupons, the observed or...

The coupon subset collection is a generalization of the classical coupon collection, where instead of selecting (with replacement) a single coupon, a subset of at most k coupons (known as a “package”) is selected in each round. In this paper, we study how to design the collection of packages and assign probabilities to the packages, so as to minimize the expected number of rounds to collect all...

With the advent of panel data on household purchase behavior, and the development of statistical procedtfres to utilize this data, firms can now target coupons to selected households with increasing accuracy and cost effectiveness. As a consequence, new avenues of competition have opened up in which firms play an active role in market segmentation. In this article, we develop an analytical fram...

Businesses (retailers) often wish to offer personalized advertisements (coupons) to individuals (consumers), but run the risk of strong reactions from consumers who want a customized shopping experience but feel their privacy has been violated. Existing models for privacy such as differential privacy or information theory try to quantify privacy risk but do not capture the subjective experience...

The overall objective of this paper is to introduce a new methodology of fitting zerocoupon yield curves. Toward this end, Chebyshev polynomials are incorporated into a quantity called the interest cumulator and then subjected to a minimisation procedure to yield parameters that subsequently maps out zero-coupon yield curves. This methodology is applied to Australian coupon bond data to estimat...

An existing coupon compression fixture was modified for testing cylindrical coupon samples of pultruded material in compression. Then a new fixture was developed for testing full-size structural shapes, which presents all the advantages of the coupon fixture. Particularly, splitting of the end of the sample is prevented while reducing the stress concentration factor at the ends, yielding compre...

Simple random coverage models, well studied in Euclidean space, can also be defined on a general compact metric space. By analogy with the geometric and discrete coupon collector's problem cover times for finite Markov chains, one expects weak concentration bound distribution of time to hold under minimal assumptions. We give two such results, fixed-radius balls other sequentially arriving rand...