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The stochastic precedence ordering with applications in sampling and testing

Part of: Distribution theory - Probability Computer system organization Sampling theory, sample surveys Circuits, networks

Published online by Cambridge University Press:  14 July 2016

Philip J. Boland ,
Harshinder Singh  and
Bojan Cukic
Philip J. Boland*
Affiliation:
National University of Ireland, Dublin
Harshinder Singh*
Affiliation:
West Virginia University
Bojan Cukic*
Affiliation:
West Virginia University
*
∗ Postal address: Department of Statistics, University College Dublin, Belfield, Dublin 4, Ireland. Email address: [email protected]
∗∗ Postal address: Department of Statistics, West Virginia University, PO Box 6330, Morgantown, WV 26506, USA.
∗∗∗ Postal address: Department of Computer Science and Electrical Engineering, Sciences Building, West Virginia University, PO Box 6109, Morgantown, WV 26506, USA.
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Abstract

Stratified and simple random sampling (or testing) are two common methods used to investigate the number or proportion of items in a population with a particular attribute. Although it is known that cost factors and information about the strata in the population are often crucial in deciding whether to use stratified or simple random sampling in a given situation, the stochastic precedence ordering for random variables can also provide the basis for an interesting criteria under which these methods may be compared. It may be particularly relevant when we are trying to find as many special items as possible in a population (for example individuals with a disease in a country). Properties of this total stochastic order on the class of random variables are discussed, and necessary and sufficient conditions are established which allow the comparison of the number of items of interest found in stratified random sampling with the number found in simple random sampling in the stochastic precedence order. These conditions are compared with other results established on stratified and simple random sampling (testing) using different stochastic-order-type criteria, and applications are given for the comparison of sums of Bernoulli random variables and binomial distributions.

Keywords

Stratified random samplingsimple random samplingpartition and subdomain testingsoftware faultstesting domainsubdomainBernoulli distributionbinomial distributionstochastic orderstochastic precedence ordermean orderarithmetic meangeometric meancomplimentary geometric mean

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62D05: Sampling theory, sample surveys 68M15: Reliability, testing and fault tolerance 94C12: Fault detection; testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 73 - 82
Copyright
Copyright © Applied Probability Trust 2004 

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