Posplošeni linearni modeli

delo diplomskega seminarja

Leon Horvat (Author), Jaka Smrekar (Mentor)

Abstract

Analiziranje in modeliranje povezav med spremenljivkami postaja vedno bolj pomembno. V delu so predstavljeni linearni posplošeni modeli in njihov razvoj iz modelov linearne regresije. Diskutirane so teoretične zahteve modelov, podrobno je predstavljena eksponentna družina porazdelitev slučajnih spremenljivk in pripadajoče naravne povezovalne funkcije. Definirane so osnovne oblike pojasnjevalnih slučajnih spremenljivk, za lažje razumevanje so podani njihovi primeri. Razloženi so tudi postopki za preverjanje prileganja gnezdenih modelov z devianco. Vse našteto je uporabljeno za gradnjo modelov prekinitev, kapitalizacij in odkupov polic življenjskega zavarovanja. Za bolj jasno sliko so opisane oblike življenjskih zavarovanj in njihova povezava s prekinitvami, kapitalizacijami in odkupi. Razčlenjeno je čiščenje in preoblikovanje podatkov, ki so bili na voljo za modeliranje. Podrobno so raziskani vplivi posameznih pojasnjevalnih slučajnih spremenljivk na proučevano spremenljivko in ugotovitve, katere spremenljivke so pomembne za napovedovanje in katere ne. Vse to omogoča zavarovalnici globlji vpogled v kompleksna razmerja v njenem portfoliu in boljšo pripravljenost na dejavnike tveganja v prihodnosti.

Keywords

matematika;posplošeni linearni modeli;linearna regresija;logistična regresija;eksponentna družina;povezovalna funkcija;devianca;življenjsko zavarovanje;prekinitev;kapitalizacija;odkup;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[L. Horvat]
UDC:	519.2
COBISS:	18429785
Views:	1128
Downloads:	400
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Generalized linear models
Secondary abstract:	Analysing and modelling relationships between variables are getting more and more important. In this work, we introduce generalized linear models, and develop them from linear regression models. We discuss theoretical assumptions for these models, and give an in-depth explanation of exponential families of distributions and the associated canonical link functions. We classify the most standard types of explanatory variables, and provide several examples for easier understanding. We explain the procedure for comparing nested models with deviance. We apply the theory described above to constructing models for lapsed, paid up, and surrendered life insurance policies. For a clearer picture, different forms of life insurance and their relationships with lapsed, paid up and surrendered policies are presented. We analyse the influences of individual explanatory variables on the response variable, and determine which explanatory observations are essential and which are not. With this, an insurance company may gain insight into complex relationships in its portfolio and better readiness for risk factors in the future.
Secondary keywords:	mathematics;generalized linear models;linear regression;logistic regression;exponential family;link function;deviance;life insurance;lapse;paid up insurance;surrender;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	31 str.
ID:	10958735