Dixie cups: sampling with replacement from a finite population

1994 ◽  
Vol 31 (4) ◽  
pp. 940-948 ◽  
Author(s):  
Chris A. J. Klaassen
Keyword(s):  
Sample Size ◽  
Random Sample ◽  
Finite Population ◽  
Asymptotic Properties ◽  
Random Sample Size ◽  
Coupon Collector’S Problem ◽  
Coupon Collector's Problem ◽  
Unequal Sampling

At which (random) sample size will every population element have been drawn at least m times? This special coupon collector's problem is often referred to as the Dixie cup problem. Some asymptotic properties of the Dixie cup problem with unequal sampling probabilities are described.

Dixie cups: sampling with replacement from a finite population

1994 ◽  
Vol 31 (04) ◽  
pp. 940-948 ◽  
Author(s):  
Chris A. J. Klaassen
Keyword(s):  
Sample Size ◽  
Random Sample ◽  
Finite Population ◽  
Asymptotic Properties ◽  
Random Sample Size ◽  
Coupon Collector’S Problem ◽  
Coupon Collector's Problem ◽  
Unequal Sampling

At which (random) sample size will every population element have been drawn at least m times? This special coupon collector's problem is often referred to as the Dixie cup problem. Some asymptotic properties of the Dixie cup problem with unequal sampling probabilities are described.

The Significance of Random Sample Size in Flow-Through Photometric Prescreening in Cervical Cytology

1976 ◽  
Vol 157 (2) ◽  
pp. 142-146 ◽  
Author(s):  
E. Sprenger ◽  
M. Schaden ◽  
D. Wagner ◽  
W. Sandritter
Keyword(s):  
Sample Size ◽  
Random Sample ◽  
Cervical Cytology ◽  
Random Sample Size ◽  
Flow Through

Limit theorems for extremes with random sample size

1998 ◽  
Vol 30 (03) ◽  
pp. 777-806 ◽  
Author(s):  
Dmitrii S. Silvestrov ◽  
Jozef L. Teugels
Keyword(s):  
Weak Convergence ◽  
Sample Size ◽  
Random Sample ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Random Sample Size ◽  
Extremal Processes ◽  
Convergence Type

This paper is devoted to the investigation of limit theorems for extremes with random sample size under general dependence-independence conditions for samples and random sample size indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems for extremal processes with random sample size indexes.

Limit Theorems for an Extended Coupon Collector's Problem and for Successive Subsampling with Varying Probabilites*

1980 ◽  
Vol 29 (3-4) ◽  
pp. 113-132 ◽  
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Asymptotic Normality ◽  
Limit Theorems ◽  
Finite Population ◽  
Waiting Times ◽  
Invariance Principles ◽  
Weak Invariance ◽  
Coupon Collector’S Problem ◽  
Asymptotic Distribution Theory ◽  
Multistage Sampling ◽  
Coupon Collector's Problem

Asymptotic normality as well as some weak invariance principles for bonus sums and waiting times in an extended coupon collector's problem are considered and incorporated in the study of the asymptotic distribution theory of estimators of (finite) population totals in successive sub-sampling (or multistage sampling) with varying probabilities (without replacement). Some applications of these theorems are also considered.

scholarly journals On weak convergence of empirical processes for random number of independent stochastic vectors

1973 ◽  
Vol 73 (1) ◽  
pp. 139-144 ◽  
Author(s):  
Pranab Kumar Sen
Keyword(s):  
Weak Convergence ◽  
Sample Size ◽  
Random Sample ◽  
Random Number ◽  
Empirical Process ◽  
Empirical Processes ◽  
Random Sample Size ◽  
Martingale Property

AbstractBy the use of a semi-martingale property of the Kolmogorov supremum, the results of Pyke (6) on the weak convergence of the empirical process with random sample size are simplified and extended to the case of p(≥1)-dimensional stochastic vectors.

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