Observations on the Geometrical Properties of Accuracy Growth in Sampling with Finite Populations

by
Constantine Stamatopoulos
FAO Fisheries Department

ISSN 0249-9345
FAO
FISHERIES
TECHNICAL
PAPER
388

Food and Agriculture Organization of the United Nations
Rome, 1999

Table of Contents


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M-40

ISBN 92-5-104341-8

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© FAO 1999

Table of Contents

PREPARATION OF THIS DOCUMENT

ABSTRACT

FOREWORD

ACKNOWLEDGMENTS

1. INTRODUCTION

2. MEASURING THE SAMPLING EFFICIENCY

2.1 Definition of accuracy
2.2 Numerical example
2.3 Practical interpretation of accuracy A

3. PROGRESSIVE SAMPLING APPROACHES

3.1 Definition of a Progressive Sampling Approach (PSA)
3.2 Accuracy curves
3.3 Overall mean accuracy of a PSA
3.4 Definition of the "Worst" PSA

4. CONVEX, FLAT AND CONCAVE POPULATIONS

4.1 Descriptive definition
4.2 Mathematical definition
4.3 Proposition concerning the Worst Overall Mean Accuracy (WOMA)

5. GLOBAL ACCURACY BOUNDARIES

5.1 The feasible domain of A-curves for flat and convex populations
5.2 The feasible domain of A-curves for all population categories
5.3 Construction of a global boundary line G(x) for all population categories
5.4 Formulae summarizing the global boundaries G(x)

6. EXPONENTIAL ACCURACY CURVES

6.1 Transformation of "hyperbolic-type" A-curves into exponential A-curves
6.2 Breakpoints of exponential A-curves and critical sample size
6.3 Observations on the exponential A-curves
6.4 The area below the exponential boundary G(x)

7. GEOMETRICAL LIMITS FOR EXPONENTIAL ACCURACY CURVES

7.1 A fundamental property of exponential A-curves
7.2 Intersection of exponential A-curves with the x=0.5 axis
7.3 Construction of a lower limit curve A_(x)

8. GEOMETRICAL LIMITS FOR INFINITE POPULATIONS

9. APPLICABILITY OF THE METHOD

10. CONCLUSIONS

11. REFERENCES

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