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Modely s náhodnými efekty v analýze přežívání
Faltus, Václav
The aim of this paper is to present an overview of the methods used in modeling survival data. Since the topic of my future Ph.D. thesis is Statistical models for correlated survival data we introduce the use of frailties as an equivalent of random effects in common statistical modeling together with its connection to correlation. Frailty model, how model with frailties is called, uses frailties as a parameter for individuals. Those who are most frail will experience an event earlier than others.
Fulltext: content.csg -  PDF
Plný tet: 0373342 - PDF
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Modelování rizika rezerv v neživotním pojištění založené na neagregovaných datech
Zimmermann, Pavel ; Kahounová, Jana (advisor) ; Cipra, Tomáš (referee) ; Jedlička, Petr (referee)
Recently the eld of actuarial mathematics has experienced a large development due to a signi cant increase of demands for insurance and nancial risk quanti cation due to the fact that the implementation of a complex of rules of international reporting standards (IFRS) and solvency reporting (Solvency II) has started. It appears that the key question for solvency measuring is determination of probability distribution of future cash ows of an insurance company. Solvency is then reported through an appropriate risk measure based e.g. on a percentile of this distribution. While as present popular models are based solely on aggregated data (such as total loss development from a certain time period), the main objective of this work is to scrutinize possibilities of modelling of the reserve risk (i.e. roughly said, the distribution of the ultimate incurred value of claims that have already happened in the past) based directly on individual claims. These models have not yet become popular and to the author's knowledge an overview of such models has not been published previously. The assumptions and speci cation of the already published models were compared to the practical experience and some inadequacies were pointed out. Further more a new reserve risk model was constructed which is believed to have practically more suitable assumptions and properties than the existing models. Theoretical aspects of the new model were studied and distribution of the ultimate incurred value (the modelled variable) was derived. An emphasis was put also on practical aspects of the developed model and its applicability in the case of industrial use. Therefore some restrictive assumptions which might be considered realistic in variety of practical cases and which lead to a signi cant simpli cation of the model were identi ed throughout the work. Furthermore, algorithms to reduce the number of the necessary calculations were developed. In the last chapters of the work, an e ort was devoted to the methods of the estimation of the considered parameters respecting practical limitations (such as missing observations at the time of modelling). For this purpose, survival analysis was (amongst other methods) applied.
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Probability calculator in MS Excel
Ginzl, Michal ; Malá, Ivana (advisor) ; Vrabec, Michal (referee)
The main aim of this thesis is to perform analytical methods for estimating the most commonly used survival distributions. There are introduced the maximum likelihood estimates of the parameters for the exponential, log-normal, gamma, logistic, Gumbel and Weibull distributions without data censored. For some distributions are mentioned probability plotting and how to estimate parameters with method of least squares or by method of moments. There are discussed tests of goodness of the best fitting distribution. Two tests are based on log-likelihood function and another on test of hypothesis. Practical part of this paper forms application programmed in VBA in MS Excel. Main part of this application includes: module for probability calculations, graphs editor and module for data analysis.
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Testování homogenity a dobré shody v analýze přežití
Timková, Jana
The present paper deals with the goodness of fit and the twosample problem related to the event-history type data. The proposed methods are derived from bayesian nonparametric approach and take advantage of MCMC estimation of the hazard rate. The technique is based on Bayes construction of martingale residuals.
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Statistical survival analysis and random point processes
Volf, Petr
The paper is devoted to statistical survival analysis, discusses different probabilistic models including the Cox model of regression for the intensity of time to failure. Then, the concept of counting processes in recalled and their models (including Cox regression) is used for characterization of random point processes of repeated events (e.g. failures and repairs).
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On regression models of survival analysis and application to grouped unemployment data
Volf, Petr
The contribution deals with the Cox's regression model and with its application to the analysis of group ed data, when both the numbers of followed objects and the numbers of observed events are summarized in discrete time periods and covariate classes. The formulation of the model and the procedure of estimation of its parameters are presented. A numerical example shows the analysis of grouped unemployment data.
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Survival analysis - probability distributions and their characteristics
Plocová, Michaela ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
This bachelor thesis is concerned with probability distributions that are used in survival analysis and characteristics of these distributions (survival function, hazard rate, probability density function, mean residual life). The aim of this thesis is to provide a summary of probability distributions and their characteristics, then to graphically represent them and show the shapes they can take in dependence on different parameters of distributions. The thesis is divided in 4 parts, the first three parts are mainly theoretical and they focus on general definitions of the characteristics, the most widely used distributions in survival analysis and mixture distributions. The last part is practical and focuses mainly on graphic representation of the characteristics for separate distributions and different values of parameters. Also, for each distribution measures of location and variability are calculated. The characteristics of mixture distributions are also graphically represented.
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