THE USE OF FINITE MIXTURES OF LOGNORMAL AND GAMMA DISTRIBUTIONS
Abstract
In the text the finite mixtures of distributions are studied with special emphasis to the models with known group membership. Component distributions are supposed to be two parameter lognormal and gamma distributions, both distributions are unimodal and positively skewed. The former distribution allows independent maximum likelihood estimates of parameters, the latter asymptotically strongly dependent estimates. Maximum likelihood method of estimation is used to estimate unknown parameters of the model - the parameters of component distributions and the component proportions from large samples. In the text large samples are treated, so the asymptotical properties of maximum likelihood estimates mentioned above are discussed with respect to the asymptotic normal bivariate distribution and standard deviances of estimated parameters. Models based on uncensored data (equivalized annual net incomes in the Czech Republic) and censored data (duration of unemployment in the Czech Republic) are analysed and particular problems connected to both estimation procedures are introduced. For both problems the model with lognormal components was found superior to the model with gamma components. All calculations are made in the program R.
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