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Compound Poisson distribution
Valentovičová, Katarína ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
Claims reserving and claims process estimation are classical problems in general insurance. Some of the statistical methods in this field are based on a compound distribution. This distribution arises as a sum of a random number of independent and identically distributed variables. This thesis deals, in particular, with the compound Poisson distribution, its properties and possible applications in general insurance. Basic theoretical properties of the distribution are derived, and parameters estimation methods are discussed. The theoretical methods are illustrated on a real data set from car insurance.
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ARFIMA time series models
Vdovičenko, Martin ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
The thesis deal with long-memory processes which are defined by several ways. The main concern is dedicated to ARFIMA model, to its basic properties and its application. Next, graphical, semiparametric and parametric estimation methods of ARFIMA parameters are described in detail. Five selected R packages are introduced that are suitable for modeling long-memory processes. We discuss their basic functions with description of input arguments and output. Finally, the application of the packages on real data is discussed according to results of~each function. Data sample comes from the Nile River and represents its yearly minimal water levels. Powered by TCPDF (www.tcpdf.org)
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Quantification of multivariate risk
Hilbert, Hynek ; Hlubinka, Daniel (advisor) ; Hudecová, Šárka (referee)
In the present work we study multivariate extreme value theory. Our main focus is on exceedances over linear thresholds. Smaller part is devoted to exce- edances over elliptical thresholds. We consider extreme values as those which belong to remote regions and investigate convergence of their distribution to the limit distribution. The regions are either halfspaces or ellipsoids. Working with halfspaces we distinguish between two setups: we either assume that the distribution of extreme values is directionally homogeneous and we let the halfspaces diverge in any direction, or we assume that there are some irre- gularities in the sample cloud which show us the fixed direction we should let the halfspaces drift out. In the first case there are three limit laws. The domains of attraction contain unimodal and rotund-exponential distributions. In the second case there exist a lot of limit laws without general form. The domains of attraction also fail to have common structure. The similar situation occurs for the exceedances over elliptical thresholds. The task here is to investigate convergence of the random vectors living in the complements of ellipsoids. For all, the limit distributions are determined by affine transformations and distribution of spectral measure. 1
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Variance and Covariance Analysis with an application to financial data
Hájková, Anna ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
This Bachelor Thesis is dedicated to analysis variance and co- variance with and application to financial data. The aim of this thesis is to inform about multidimensional ANOVA and to show its connection with one- dimensional ANOVA, which is a part of standart statistical textbooks. Other part describes the analysis of covariance. For the better understanding, most of methods are applicated to financial data in the program Mathematica 8.0 1
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Selected methods of time series analysis with STATISTICA
Indrová, Magdalena ; Hudecová, Šárka (advisor) ; Zichová, Jitka (referee)
This work deals with the use of STATISTICA software for the basic analysis of time series. The thesis is focused on time series decomposition, mainly on the trend elimination. First, the basic methods of the analysis are described theoretically, namely, trend modeling using mathematical curves (polynomial, exponential, logistic and Gompertz) and adaptive approach (moving averages, simple exponential smoothing and Holt's method). These methods are then applied to three selected data sets (unnamed bank's balance sheet from 1998 to 1993, ship construction trends between 1820 and 1997, and CZK/EUR Exchange rate from 1998 to 2012). All analytical procedures are described in detail and individual program outputs are thoroughly explained and commented.
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Survival analysis with STATISTICA
Kaderjáková, Zuzana ; Hudecová, Šárka (advisor) ; Hurt, Jan (referee)
Survival analysis is a separate statistical area. This paper discusses the~interpretation of basic concepts, principles and methods used and implemented in the software STATISTICA. First, we introduce censoring and ways of characterizing a distribution of survival time. We present Kaplan-Meier estimate of a survival function and also a method of mortality tables. Later, we discuss basic methods of comparison of the survival time distribution in two groups and their suitability for different situations. The paper also deals with application of the survival analysis methods in the financial sector, where we introduce Cox proportional hazards model. Finally, we apply theoretical knowledge to a real data set.
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Survival function estimation
Chrenko, Jakub ; Komárek, Arnošt (referee) ; Hudecová, Šárka (advisor)
Nazev prace: Odhady funkcr pfeziti Autor: Jakub Chrenko Kalodra: Katcdra pravdepodobnosti a mateinaticke statistiky Vedouci ba.ka.la.fske pra.ce: Mgr. Sarka Dosla e-mail vedouciho: dosla'ii'karlin.mff.cimi.cz Abstrakt: V pfedlozene pnici so zabyvame funkci pfeziti a jejuni odharly. Popsany jsou jak paramrtrirke, tak i neparamelrickc' pf ist upv. V obou piipa- deeh je pfihledimto k pfi'padncuiu ccnzorovanf clat. NoiJaramotricke rriotody iifkladon /adno pozadavky ua rozdrloni dat, a proto jsou uuiverzalne po- uzitcliic. Z tcchlo nictod uvadi'nir Z(^jmciH^ Ka,pkui-M(ucruv odhad fiinkcc pfcziti, jchoz zakladni vlastnosti jsou popsany. Ziiu'iiena je l.ra analyza ta- bulck unirtnosti. Parauietricke piist.upy j)rcdpokl;idaji koiikrntui tvar tno- rciickclio rozdeleiii sludovniio nahodric voliriny. Z nojcast.eji pouzivanycii rozdclonf Tivadinic oxporinucialui, Woilnilluvo a logaritniicko iioriualni. V za- vc.i'u prac'c; jsou tyt.o inctody poT'Oviiauy a ilustrovauy ua koukretui'm da- tovom souboru a poinoci simulaci. Klfcova slova: Fuiikcc })feziti, hazard, Kaplan-Mcicruv odhad, rouzorovana dat.n Title: Estiiua.tioii oi' Survivalship Function Author: Jakub Chronko Department: Department of Probability and Mathematical statistics Supervisor: Mgr. Snrka Dosla Supervisor's e-mail address: doslaCO'karliii.iiifl.ciuii.cz...
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