Fitting Finite Mixture Model (FMM) to Frequency Data
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Date
OCTOBER, 2016
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Abstract
One of the main variables needed in analyzing quantitative growth, mortality,
and stock assessment models in fishery has been age data. Unfortunately, age as
the biological measure of time is not readily available in Ghana and other tropical
countries. Also, the graphical based methods used by most fishery scientists to
dissect and estimate demographic parameters from fishery length frequency data
(a viable substitute for the age data) makes statistical inference unreliable. In
this work, the computational method of FMM is used to decompose the 2014 yellowfin
tuna population into components (age-groups) and the estimates of each
component obtained by the Maximum Likelihood (ML) method via Expectation
Maximization (EM) and Newton Raphson (NR) algorithms. Based on the size
selection in this fishery, it could be infered that the yellowfin tuna population
consists of five subpopulations. The mixing proportions for successive age groups
increase continuously until at least the fourth component. The difference in the
continuous increment in the mean-lengths is at least twice the standard deviations.
For efficient decomposition and estimation of the mixture parameters, the
study recommeds the FMM and ML method via EM and NR algorithms over
traditional graphical methods.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fulfillment of the requirement for the Degree
of Master of Science in Industrial Mathematics.