Conventional and adjusted measures of mortality, measures of fertility, measures of morbidity. Demographic characteristics and trends of selected countries.
Evaluation of demographic data. Projections for stable and stationary populations. Actuarial applications of demographic characteristics and trends.
Stationary and non-stationary of series: removal of trend and seasonality by differencing. Moments and auto-correlation. Models: simple AR and MA models (mainly AR(1), MA(1)): moments and auto-correlations; the conditions of stationarity: invertibility. Mixed (ARMA) models, and the AR representation of MA and ARMA models. Yule-Walker equations and partial auto-correlations (showing forms for simple AR, MA models). Examples showing simulated series from such processes, and sample auto-correlations and partial auto-correlations.
Preliminary concepts: the nature of a stochastic process, parameter space and state space. Markov processes and Markov chains. Renewal processes. Stationary processes. Markov chains: First order and higher order transition probabilities. Direct computation for two-state Markov chains. The Chapman-Kolmogorov equations. Unconditional state probabilities. Limiting distribution of a two-state chain. Classification of states. Closed sets and irreducible chains. Various criteria for classification of states. Queuing processes: characteristics and examples. Differential equations for a generalised queuing model. M/M/1 and M/M/S queues: characteristics of queue length, serving times and waiting time distributions. Inter-arrival times and traffic intensity. Applications to traffic flow and other congestion problems.
The course is specifically designed to introduce students to multivariate techniques. It helps students to handle multivariate data effectively. Specific areas include: Structure of multivariate data. Inferences about multivariate means - Hotelling’s ; likelihood ratio tests, etc. Comparisons of several multivariate means - paired comparisons; one-way MANOVA; profile analysis. Principal component analysis - graphing; summarizing sample variation, etc. Factor analysis. Discriminant analysis - separation and classification for two populations; Fisher’s discriminant function; Fisher’s method for discriminating among several populations Cluster analysis - hierarchical clustering; non-hierarchical clustering; multi-dimensional scaling.
Further methods for discrete data: examples and formulation - binomial, multinomial and Poisson distributions. Comparison of two binomials; McNeyman’s test for matched pairs; theory and transformations of variables; multiple linear regression; selection of variables ; use of dummy variables. Introduction to logistic regression and generalized linear modeling. Non-parametric methods. Use of least squares principle; estimation of contrasts, two-way crossed classified data.
Estimation theory - unbiased estimators; efficiency; consistency; sufficiency; robustness. The method of moments. The method of maximum likelihood. Bayesian estimation - prior and posterior distributions; Bayes’ theorem; Bayesian significant testing and confidence intervals. Applications - point and intervals. Estimations of means, variances, differences between means, etc. Hypothesis testing theory - test functions; the Neyman - Pearson Lemma; the power function of tests, Likelihood ratio test.
Report writing and presentation ― organization, structure, contents and style of report. Preparing reports for oral presentation. Introduction to word processing packages, e.g., word for windows and latex. Single- and two-sample problems; Poisson and binomial models. Introduction to the use of generalized linear modeling in the analysis of binary data and contingency tables. Simple and multiple linear regression methods; dummy variables; model diagnostics; one and two-way analysis of variance. Data exploration method - summary and graphical displays. Simple problems in forecasting.
This course will introduce students to the sampling methods. The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size;
estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc. Stratified random sampling - proportional and optimum allocations.
Cluster sampling, systematic sampling, multistage sampling.
This course will introduce students to the sampling methods. The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size; estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc. Stratified random sampling - proportional and optimum allocations. Cluster sampling, systematic sampling, multistage sampling.
Introduction to Statistical Software: Eg. SPSS, Minitab, R, Matlab. Statistical data – Data from designed experiments; sample surveys; observational studies. Data exploration - sample descriptive techniques: measures of location and spread; correlation, etc. Diagrammatic representation of data: the histogram; stem - and leaf -; box-plot; charts, etc. Tabulation, interpretation of summary statistics and diagrams. Regression and Correlation Analysis: Simple Linear Regression. Interpretation of coefficients, Correlation and coefficient of determination. One-way ANOVA.
