Estimation of finite mixture densities with applications in data networks

Finite Mixture Models (FMM) are probabilistic combinations of a finite set of probability distributions. FMMs have numerous applications in signal analysis (e.g. in communications and network performance modeling), in medicine (e.g. in diagnosis of ailments such as schizophrenia and diabetes), in economics (e.g. in risk analysis), and many other areas.; Two types of finite mixtures are studied in this dissertation: the Gaussian mixture model (GMM) and the hyperexponential density. The problem of estimating the parameters of a GMM from samples of data is old, and typically the Expectation-Maximization (EM) algorithm is used. The EM algorithm has several shortcomings, most notably a slow convergence rate. Algorithms are developed in this dissertation which serve as alternatives to the EM algorithm for certain cases of mixture densities. Estimators for the mixing proportions and common component variance are developed for a GMM from samples of data, given that the component means are known. This problem is motivated by introducing a practical application in digital wireless communications. The estimators use nonlinear functions (trigonometric and hyperbolic) of the data. Linear equations in the unknown parameters are constructed which are guaranteed to have a solution. The coefficients in the linear equations are functions of the data. The estimators converge to the actual parameter values with probability one and are asymptotically normal. The estimators are easily implemented. Simulation results are also presented.; Two algorithms are developed for estimating the unknown mixing proportions, component means and common component variance of a GMM, from data samples. The algorithms make use of nonlinear functions of the data, an estimate of the cumulative distribution function (cdf) of the GMM, and nonlinear unconstrained optimization techniques. These algorithms are simple, efficient and simulation results show that they give fairly accurate results.; Finally, two algorithms are developed for estimating the unknown steady state probabilities and component rates of a hyperexponential density, from data samples. The algorithms use nonlinear data transformations, an estimate of the hyperexponential cdf and nonlinear unconstrained optimization methods. The algorithms are efficient and easily implemented. Simulation results also show that they give accurate estimates.