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Pričakovana življenjska doba : delo diplomskega seminarja
ID Prelog, Saša (Author), ID Dolžan, David (Mentor) More about this mentor... This link opens in a new window

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Abstract
V diplomskem delu so najprej na kratko razloženi pojmi povezani z modeli preživetja, za tem pa še pričakovana preostala življenjska doba ob smrti in formula za njen izračun. Nadalje je opisan prvi modela preživetja -- Gompertz-Makehamova jakost smrtnosti, ki je sestavljena iz Gompertzove komponente, ki je odvisna od starosti, in Makehamove komponente, ki ni. Parametre tega modela ponavadi izračunamo z metodo najmanjših kvadratov iz podatkov prejšnjih let. Nato je predstavljen Lee-Carter model, pri katerem potrebujemo za napoved jakosti smrtnosti napovedati vrednost samo enega časovnega parametra $k_{s}$. Parametre tega modela določimo s pomočjo singularnega razcepa na podatkih za neko časovno obdobje. Nato lahko napovemo parameter $k_{s}$ s pomočjo ARIMA metod. Nazadnje je predstavljena še CH funkcija preživetja, ki je sestavljena iz komponente mladosti do odraslosti in komponente starih do zelo starih. Parametre za ta model izračunamo z metodo najmanjših kvadratov iz tablic smrtnosti in jih za naslednja leta napovemo s pomočjo AR metod nižjega reda. Končna primerjava opisanih modelov med sabo razkrije, da večinoma CH funkcija preživetja kaže boljše prileganje podatkom in natančnejše napovedi kot preostala dva modela.

Language:Slovenian
Keywords:Modeli preživetja, Pričakovana življenjska doba, Gompertz-Makehamova jakost smrtnosti, Lee-Carter model, CH funkcija preživetja
Work type:Bachelor thesis/paper
Organization:FMF - Faculty of Mathematics and Physics
Year:2020
PID:20.500.12556/RUL-119738 This link opens in a new window
UDC:519.2
COBISS.SI-ID:58094339 This link opens in a new window
Publication date in RUL:11.09.2020
Views:1110
Downloads:108
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Secondary language

Language:English
Title:Expected lifespan
Abstract:
In this diploma first the concepts in connection to survival models are shortly explained, as well as an average expected remaining lifespan at the moment of death and the formula to calculate it. Then the first survival model is described -- the Gompertz-Makeham force of mortality is composed of an age dependent Gompertz component and an age independent Makeham component. Parameters for this model are calculated from data of previous years, typically using the method of least squares. The Lee-Carter model is explained next. To get a forecast of the force of mortality from this model, we only need to forecast the one time parameter $k_{s}$. Parameters for this model are calculated using the singular value decomposition on time period data. Afterwards the parameter $k_{s}$ is forecast using ARIMA methods. Lastly the CH function of survival is explained. It consists of a youth to adulthood component and an old to oldest old component. Its parameters are calculated using the least squares method on mortality tables and forecast using lower-order AR methods. Finally a comparison of all three models reveals that the CH function of survival fits the data better and has more accurate forecasts than the other two models.

Keywords:Survival models, Expected lifespan, Gompertz-Makeham force of mortality, Lee-Carter model, CH survival function

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