Table of Contents

1 General introduction.- 1.1 Introduction.- 1.2 Some applications of finite mixture distributions.- 1.3 Definition.- 1.4 Estimation methods.- 1.4.1 Maximum likelihood.- 1.4.2 Bayesian estimation.- 1.4.3 Inversion and error minimization.- 1.4.4 Other methods.- 1.4.5 Estimating the number of components.- 1.5 Summary.- 2 Mixtures of normal distributions.- 2.1 Introduction.- 2.2 Some descriptive properties of mixtures of normal distributions.- 2.3 Estimating the parameters in normal mixture distributions.- 2.3.1 Method of moments estimation.- 2.3.2 Maximum likelihood estimation.- 2.3.3 Maximum likelihood estimates for grouped data.- 2.3.4 Obtaining initial parameter values for the maximum likelihood estimation algorithms.- 2.3.5 Graphical estimation techniques.- 2.3.6 Other estimation methods.- 2.4 Summary.- 3 Mixtures of exponential and other continuous distributions.- 3.1 Exponential mixtures.- 3.2 Estimating exponential mixture parameters.- 3.2.1 The method of moments and generalizations.- 3.2.2 Maximum likelihood.- 3.3 Properties of exponential mixtures.- 3.4 Other continuous distributions.- 3.4.1 Non-central chi-squared distribution.- 3.4.2 Non-central F distribution.- 3.4.3 Beta distributions.- 3.4.4 Doubly non-central t distribution.- 3.4.5 Planck's distribution.- 3.4.6 Logistic.- 3.4.7 Laplace.- 3.4.8 Weibull.- 3.4.9 Gamma.- 3.5 Mixtures of different component types.- 3.6 Summary.- 4 Mixtures of discrete distributions.- 4.1 Introduction.- 4.2 Mixtures of binomial distributions.- 4.2.1 Moment estimators for binomial mixtures.- 4.2.2 Maximum likelihood estimators for mixtures of binomial distributions.- 4.2.3 Other estimation methods for mixtures of binomial distributions.- 4.3 Mixtures of Poisson distributions.- 4.3.1 Moment estimators for mixtures of Poisson distributions.- 4.3.2 Maximum likelihood estimators for a Poisson mixture.- 4.4 Mixtures of Poisson and binomial distributions.- 4.5 Mixtures of other discrete distributions.- 4.6 Summary.- 5 Miscellaneous topics.- 5.1 Introduction.- 5.2 Determining the number of components in a mixture.- 5.2.1 Informal diagnostic tools for the detection of mixtures.- 5.2.2 Testing hypotheses on the number of components in a mixture.- 5.3 Probability density function estimation.- 5.4 Miscellaneous problems.- 5.5 Summary.- References.