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Application of Nonlinear Programming Algorithms to Some Optimum Stratification Problem

Application of Nonlinear Programming Algorithms to Some Optimum Stratification Problem Mathematical programming is a useful approach in solving the various problems in the statistical fields. In this paper, we will discuss the use of general nonlinear programming algorithms to the determination of the optimum stratification points and minimum variances in the case of estimating the population means for some typical distributions. Three sample allcoations are considered for the normal, exponential, equilateral triangular and rightangled triangular distributions. Efficiency of each sample allocation and gains of the number of strata are examined. Furthermore, relations between the optimum sample size and the number of strata are considered for some cost function. Results obtained here are applicable to the case of repetitive survey. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Behaviormetrika Springer Journals

Application of Nonlinear Programming Algorithms to Some Optimum Stratification Problem

Taguri, Masaaki; Sakakibara, Osami
Behaviormetrika , Volume 3 (3) – Feb 15, 1976
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16 pages

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Publisher
Springer Journals
Copyright
Copyright
Subject
Statistics; Statistical Theory and Methods; Statistics for Business, Management, Economics, Finance, Insurance; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
ISSN
0385-7417
eISSN
1349-6964
DOI
10.2333/bhmk.3.57
Publisher site
See Article on Publisher Site

Abstract

Mathematical programming is a useful approach in solving the various problems in the statistical fields. In this paper, we will discuss the use of general nonlinear programming algorithms to the determination of the optimum stratification points and minimum variances in the case of estimating the population means for some typical distributions. Three sample allcoations are considered for the normal, exponential, equilateral triangular and rightangled triangular distributions. Efficiency of each sample allocation and gains of the number of strata are examined. Furthermore, relations between the optimum sample size and the number of strata are considered for some cost function. Results obtained here are applicable to the case of repetitive survey.

Journal

Behaviormetrika – Springer Journals

Published: Feb 15, 1976

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