Invariance Principles for the Coupon Collector's Problem: A Martingale Approach.

Abstract

For the coupon collector's problem, invariance principles for the partial sequence of bonus sums after n coupons as well as for the waiting times to obtain the bonus sum t are studied through a construction of a triangular array of martingales related to these sequences and verifying the invariance principles for these martingales. This approcah provides simpler and neater proofs than given in Rosen (1969, 1970) and strengthens his convergence of finite dimensional results to those of weak invariance principles. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1976
Accession Number
ADA036356

Entities

People

  • Pranab Kumar Sen

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accumulators
  • Asymptotic Normality
  • Convergence
  • Data Science
  • Information Science
  • Invariance
  • Mathematics
  • New York
  • Normality
  • North Carolina
  • Probability
  • Random Variables
  • Sequences
  • Statistics
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Materials Science and Engineering.
  • Mathematical Modeling and Probability Theory.