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Statistical Classification by means of generalized linear models
Sladká, Vladimíra ; Mrázková, Eva (referee) ; Michálek, Jaroslav (advisor)
The goal of this thesis is introduce the theory of generalized linear models, namely probit and logit model. This models are especially used for medical data processing. In our concrete case these mentioned models are applied to data file obtained in teaching hospital Brno. The aim is statically analyzed immune response of child patients in dependence of twelve selected types of genes and find out which combinations of these genes influence septic state of patients.
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ADVANCED REGRESSION MODELS
Rosecký, Martin ; Popela, Pavel (referee) ; Bednář, Josef (advisor)
This thesis summarizes latest findings about municipal solid waste (MSW) modelling. These are used to solve multivariable version of inverse prediction problem. It is not possible to solve such problem analytically, so heuristic framework using regression models and data reconciliation was developed. As a side product, models for MSW modelling using PCA (Principal Component Analysis) and LM (Linear Model) were created. These were compared with heuristic model called RF (Random Forest). Both of these models were also used for per capita MSW modelling. Theoretical parts about generalized linear models, data reconciliation and nonlinear programming are also included.
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ADVANCED REGRESSION MODELS
Rosecký, Martin ; Popela, Pavel (referee) ; Bednář, Josef (advisor)
This thesis summarizes latest findings about municipal solid waste (MSW) modelling. These are used to solve multivariable version of inverse prediction problem. It is not possible to solve such problem analytically, so heuristic framework using regression models and data reconciliation was developed. As a side product, models for MSW modelling using PCA (Principal Component Analysis) and LM (Linear Model) were created. These were compared with heuristic model called RF (Random Forest). Both of these models were also used for per capita MSW modelling. Theoretical parts about generalized linear models, data reconciliation and nonlinear programming are also included.
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Aggregate loss models with dependent frequency and severity
Čápová, Petra ; Mazurová, Lucie (advisor) ; Zichová, Jitka (referee)
In non-life insurance, the independence between the number and size of claims is usually assumed. However, this thesis shows that the assumption of independence can be omitted. We deal with the dependency modeling between frequency and severity of claims. For including the dependence to the total claims model, we consider two methods. The first method uses generalized linear models and the second method used in the thesis is based on dependence modeling by copulas. We also perform a model with independent frequency and severity of claims. This model is compared with the described methods in the simulation part of the thesis. We include dependency on explanatory (rating) variables in all of these models. 1
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Pricing in non-life insurance
Ondrušková, Markéta ; Mertl, Jakub (advisor) ; Mazurová, Lucie (referee)
The aim of this thesis is to determine the premium of motor third party liability insurance. Thesis explores both direct approach to premium cal- culation and calculation using separately calculated claims frequency and claims severity. Emphasis is put on the use of generalized linear models whose theory is also present. Described approaches to calculation are applied on real world data, compared with each other and then final model for premium calculation is selec- ted. Premium is determined with the inclusion of IBNR reserves and expenses. Keywords: generalized linear model, claims frequency, claims severity, net pre- mium, gross premium, motor third party liability insurance, bonus-malus. 1
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Claims count modeling in insurance
Škoda, Štěpán ; Branda, Martin (advisor) ; Pešta, Michal (referee)
1 Abstract: The present work investigates techniques of insurence ratemaking accor- ding to the claims counts of policyholders on the basis of information contained in policies. At the beginning, we provide a closer examination of the theory of genera- lized linear models, which have wide range of applications in the field of actuarial modeling. The second chapter presents the basic Poisson regression model as well as some particular verification methods. Specifically, deviance and Wald test could be found here and furthermore also important results for residuals. The third chapter contains information on alternative approaches to modeling the claim frequencies and at the end the GEE method, that can be applied in case of panel data, is de- scribed. The numerical study based on real insurace data in last part of this diploma thesis illustrate's previously described techniques which were obtained with the help of statistical software SAS.
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Variability estimation of development triangles in nonlife insurance
Havlíková, Tereza ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
The aim of this thesis is to describe calculation methods for variability esti- mation of claims reserve in non-life insurance. The thesis focuses on three main categories of models: Mack's stochastic Chain-Ladder, generalized linear models and bootstrap. Both the theoretical and also the empirical parts are included. Empirical part is devoted to application of all the models described above on both real and simulated data. 1
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Traditional and modern approaches to pricing in nonlife insurance
Vojtěch, Jonáš ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
Title: Traditional and modern approaches to pricing in nonlife insurance Abstract: This thesis deals with the theory and implementation of generalized linear models in the area of pricing of non-life insurance and subsequent optimalization of rates. Using the generalized linear models it is possible to estimate expected value and variance of compound distribution of total claims made according to insurance policy during definite time period. The next step is to build an optimalization model and describe several methods how to determine rates that lead to optimal distribution of safety margins within insurance policies in particular risk groups. Represented approaches how to calculate insurance premiums are numerically illustrated on simulated data in concluding parts of the thesis.
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Statistical Classification by means of generalized linear models
Sladká, Vladimíra ; Mrázková, Eva (referee) ; Michálek, Jaroslav (advisor)
The goal of this thesis is introduce the theory of generalized linear models, namely probit and logit model. This models are especially used for medical data processing. In our concrete case these mentioned models are applied to data file obtained in teaching hospital Brno. The aim is statically analyzed immune response of child patients in dependence of twelve selected types of genes and find out which combinations of these genes influence septic state of patients.
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Mathematical modelling in general insurance
Zajíček, Jakub ; Bílková, Diana (advisor) ; Bohatová Chládková, Dana (referee)
This diploma thesis deals with the mathematical models in general insurance. The aim of this thesis is to analyse selected mathematical models that are widely used in general insurance for the estimation of insurance portfolio statistics, pricing and the regulatory capital requirement calculation. Claim frequency models, claim severity models, aggregate loss models and generalized linear models are analysed. This thesis consists of a theoretical and a practical part. The theoretical part contains description of selected models. Described models are then applied to a real dataset in the practical part. The real dataset modelling was performed using the statistical software R. It has been proved that maximum likelihood parameter estimations are of better quality than the method of moments or quantile method estimations. The results of aggregate loss distribution computational methods are comparable. This comparability is mostly caused by a large number of observations. In the context of tariff analysis it was found that the most significant factors are driver's age and the driver's area of residence.
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