Estimating life tables from Leslie population models

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This thesis considers the modelling of life table models for Ghana, when her population becomes stable in the future. To do this, a Leslie matrix for Ghana is first determined. The Leslie model (which is an age-structured population projection model) is used to find the stable age distribution, which forms the basis for actuarial computations. The dominant eigenvalue which represents the asymptotic growth rate of the population and the corresponding eigenvector of the Leslie matrix which represents the stable population is also determined. The stable population is used to compute life tables for Ghana, and the life tables are then compared with other life tables to see the disparities. A mortality model is estimated by fitting the survival function from the life table to other already existing mortality models. Ghana’s mortality model has thus been found to follow the Modified De Moivre distribution. Despite the lack of accurate data, the Leslie model has nevertheless been helpful in generating life tables for Ghana. It has been found that Ghana’s population would attain stability by the year 2030, and in 2030 the total population has been estimated to be 43.8 million comprising 49.6 percent males and 50.4 percent females. When Ghana attains this stable age distribution, life expectancy would be 58 years for males and 60 years for females.
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 Philosophy in Acturial Science, 2015