by

**Constantine Stamatopoulos**

FAO Fisheries Department

ISSN 0249-9345

**FAO
**

**Food ****and ****Agriculture ****Organization ****of
****the ****United ****Nations
Rome, 1999 **

The designations employed and the presentation of material in this publication do not imply the expression of any opinion whatsoever on the part of the Food and Agriculture Organization of the United Nations concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. |

M-40

ISBN 92-5-104341-8

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise, without the prior permission of the copyright owner. Applications for such permission, with a statement of the purpose and extent of the reproduction, should be addressed to the Director, Information Division, Food and Agriculture Organization of the United Nations, Viale delle Terme di Caracalla, 00100 Rome, Italy.

© **FAO 1999**

** 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)

5.1 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**