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Modelling mortality differentials by age
Šuléřová, Natálie ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This diploma thesis deals with sex-specific mortality modelling, that is modelling in two populations - female and male, with emphasis on models considering the inter- dependence between these populations. Four models were theoretically described in the thesis - independent Lee-Carter model, the common factor model, the augmented com- mon factor model and the credibility model. All models were then applied to real mortality data in the female and male population of the Czech Republic and compared with each other. Mortality rates for Czech females and males were predicted by selected models. Finally, the effect of including a common factor in mortality modelling was analyzed in comparison with independent modelling in both populations as the difference in a lia- bility value arising from selected life insurance products. 1
Markov binomial model
Šuléřová, Natálie ; Hudecová, Šárka (advisor) ; Dvořák, Jiří (referee)
In this thesis we study the Markov chain binomial model, which generalizes the standard binomial distribution. Instead of the sum of independent random vari- ables, we consider the sum of random variables that form a stationary Markov chain. The goal of this thesis is to describe this model along with its proper- ties, such as the expected value, variance and probability generating function. A part of this thesis is dedicated to estimating parameters of this model using the method of moments and the maximum likelihood estimation. The accuracy of the methods is compared in a simulation study and obtained results are dis- cussed. The presented model is then applied on a real dataset based on rate of alcohol-impaired car accidents.

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2 Šuleřová, Nikol
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