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RESEARCH ARTICLE
Contents Vol 56(5)

Estimating age composition using the Fredholm first-kind equation

V. S. Troynikov A B and S. G. Robertson A
+ Author Affiliations
- Author Affiliations

A Marine and Freshwater Systems, Research and Development Division, Department of Primary Industries, PO Box 114, Queenscliff, Vic. 3225, Australia.

B Corresponding author. Email: vladimir.troynikov@dpi.vic.gov.au

Marine and Freshwater Research 56(5) 745-751 https://doi.org/10.1071/MF04152
Submitted: 13 July 2004  Accepted: 6 April 2005   Published: 21 July 2005

Abstract

Estimation of age composition was considered in the context of non-parametric mixture distribution problems. The problem was formulated as a Fredholm first-kind equation with respect to the distribution function of age. The solution of the equation was obtained using methods for ‘ill-posed problems’. The approach is able utilise single and multi-dimensional empirical distributions of age-dependant variables. School whiting (Sillago flindersi) fish length and otolith weight measurements were used in a numerical example. Different combinations and sample sizes of input data were used for numerical error analysis.

Extra keywords: age distribution, age-length key, cohort, Fredholm equation, ill-posed problems, mixture distribution problem, population.


Acknowledgments

We would like to thank Professor Peter Hall for reviewing of the method in context of the mixture distribution problems. We would like to thank Dr Steven Campana for suggesting the use of age/otolith weights data for numerical cohort reconstruction. Staff at the Central Ageing Facility, Primary Industries Research Victoria are also acknowledged for the supply of the age and otolith data that was used in these experiments. We thank to the Guest Editor for the Otolith Symposium Special Issue and two anonymous reviewers for helpful suggestions that improved the quality of the manuscript.


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