Fitting Finite Mixture Model (FMM) to Frequency Data

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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.
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.