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An Application of Quantile Functions in Probability Model Constructions of Wage Distributions
Pavelka, Roman ; Kahounová, Jana (advisor) ; Vrabec, Michal (referee) ; Pacáková, Viera (referee)
Over the course of years from 1995 to 2008 was acquired by Average Earnings Information System under the professional gestation of the Czech Republic Ministry of Labor and Social Affairs wage and personal data by individual employees. Thanks to the fact that in this statistical survey are collected wage and personal data by concrete employed persons it is possible to obtain a wage distribution, so it how this wages spread out among individual employees. Values that wages can be assumed in whole wage interval are not deterministical but they result from interactions of many random influences. The wage is necessary due to this randomness considered as random quantity with its probability density function. This spreading of wages in all labor market segments is described a wage distribution. Even though a representation of a high-income employee category is evidently small, one's incomes markedly affect statistically itemized average wage level and particularly the whole wage file variability. So wage employee collections are distinguished by the averaged wage that exceeds wages of a major employee mass and the high variability due to great wage heterogeneity. A general approach to distribution of earning modeling under current heterogeneity conditions don't permit to fit by some chosen distribution function or probably density function. This leads to the idea to apply some quantile approach with statistical modeling, i.e. to model an earning distribution with some appropriate inverse distributional function. The probability modeling by generalized or compound forms of quantile functions enables better to characterize a wage distribution, which distinguishes by high asymmetry and wage heterogeneity. The application of inverse distributional function as a probability model of a wage distribution can be expressed in forms of distributional mixture of partial employee's groups. All of the component distributions of this mixture model correspond to an employee's group with greater homogeneity of earnings. The partial employee's subfiles differ in parameters of their component density and in shares of this density in the total wage distribution of the wage file.
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Application of generalized linear model for mixture distributions
Pokorný, Pavel ; Malá, Ivana (advisor) ; Pavelka, Roman (referee)
This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.
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