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Poisson-modellering av dödsbränder i Sverige

Hedberg, Jonatan LU and Lindahl, Elna LU (2017) STAH11 20162
Department of Statistics
Abstract (Swedish)
Denna uppsats är skriven på uppdrag av Lunds tekniska högskola och Myndigheten för samhällsskydd och beredskap. Uppdraget består av att modellera antalet dödsbränder som sker i Sverige över tid, samt undersöka ifall det har skett någon signifikant förändring. Detta görs utifrån ett antagande om att dödsbränder är Poisson-fördelade, därmed betraktas antalet dödsbränder över tid som en Poisson-process. Frågeställningen kan då besvaras genom att studera om, och i så fall hur, processens intensitet förändras över tid. Intensiteten modelleras med Poisson-regression med tidskovariat. Vi använder en modell med kvartalsdata som innehåller säsongskomponenter, en linjär trend och en brytpunkt i mitten av 2012. Den linjära trenden har en negativ... (More)
Denna uppsats är skriven på uppdrag av Lunds tekniska högskola och Myndigheten för samhällsskydd och beredskap. Uppdraget består av att modellera antalet dödsbränder som sker i Sverige över tid, samt undersöka ifall det har skett någon signifikant förändring. Detta görs utifrån ett antagande om att dödsbränder är Poisson-fördelade, därmed betraktas antalet dödsbränder över tid som en Poisson-process. Frågeställningen kan då besvaras genom att studera om, och i så fall hur, processens intensitet förändras över tid. Intensiteten modelleras med Poisson-regression med tidskovariat. Vi använder en modell med kvartalsdata som innehåller säsongskomponenter, en linjär trend och en brytpunkt i mitten av 2012. Den linjära trenden har en negativ koefficient, antalet dödsbränder minskar alltså succesivt under perioden. Brytpunkten år 2012 indikerar att intensiteten minskar med ca 20%. En nedgång konfirmeras även med ett t-test. Vi finner också att modellen, med ett 99% konfidensintervall, fångar upp variationen i processen med undantag för extremvärden. (Less)
Abstract
The authors of this thesis were tasked with modelling fatal fires in Sweden to answer the question, whether the quarterly number of fires has changed over time. The usage of the Poisson distribution in modelling accidents and mortalities is well attested. Problems arise when measuring the number of fire related mortalities, as several deaths can be attributed to one fire. This violates the assumption of independence of the Poisson distribution. To avoid this, the number of fatal fires is modelled.

The number of fires leading to mortalities is approached as a Poisson point process. This allows us to answer the question posed by looking at if and how the intensity of the process varies, which is done by applying Poisson regression with... (More)
The authors of this thesis were tasked with modelling fatal fires in Sweden to answer the question, whether the quarterly number of fires has changed over time. The usage of the Poisson distribution in modelling accidents and mortalities is well attested. Problems arise when measuring the number of fire related mortalities, as several deaths can be attributed to one fire. This violates the assumption of independence of the Poisson distribution. To avoid this, the number of fatal fires is modelled.

The number of fires leading to mortalities is approached as a Poisson point process. This allows us to answer the question posed by looking at if and how the intensity of the process varies, which is done by applying Poisson regression with time covariates. The data used comes from the Swedish Civil Contingency Agency. It contains, among others, monthly data of all fatal fires from 1999 to 2016. The monthly data varies to a great extent, which makes modelling difficult. For that reason, the months are summed into quarters. Regressing on the quarterly data, a model containing seasonal components, a linear trend and a breakpoint in mid-2012 is successfully fitted. Winter has, according to the model a positive effect on the incident ratio, while summer has a negative effect. The linear trend acts negatively, meaning that the rate of fatal fires is decreasing. Lastly, the breakpoint, pushes the incident rate down with approximately 20%. With a 99% confidence interval, the model predicts the rate of fatal fires, except for extreme values. To corroborate a decline in the number of fatal fires after mid-2012, a t-test is performed. (Less)
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author
Hedberg, Jonatan LU and Lindahl, Elna LU
supervisor
organization
course
STAH11 20162
year
type
M2 - Bachelor Degree
subject
keywords
Poisson-regression, Inhomogen Poisson-process, överspridning, dödsbränder, olycksstatistik, Inhomogenous Poisson-process, overdispersion, fatal fires, accident data
language
Swedish
id
8901194
date added to LUP
2017-04-12 11:15:57
date last changed
2017-04-12 11:15:57
@misc{8901194,
  abstract     = {The authors of this thesis were tasked with modelling fatal fires in Sweden to answer the question, whether the quarterly number of fires has changed over time. The usage of the Poisson distribution in modelling accidents and mortalities is well attested. Problems arise when measuring the number of fire related mortalities, as several deaths can be attributed to one fire. This violates the assumption of independence of the Poisson distribution. To avoid this, the number of fatal fires is modelled.

The number of fires leading to mortalities is approached as a Poisson point process. This allows us to answer the question posed by looking at if and how the intensity of the process varies, which is done by applying Poisson regression with time covariates. The data used comes from the Swedish Civil Contingency Agency. It contains, among others, monthly data of all fatal fires from 1999 to 2016. The monthly data varies to a great extent, which makes modelling difficult. For that reason, the months are summed into quarters. Regressing on the quarterly data, a model containing seasonal components, a linear trend and a breakpoint in mid-2012 is successfully fitted. Winter has, according to the model a positive effect on the incident ratio, while summer has a negative effect. The linear trend acts negatively, meaning that the rate of fatal fires is decreasing. Lastly, the breakpoint, pushes the incident rate down with approximately 20%. With a 99% confidence interval, the model predicts the rate of fatal fires, except for extreme values. To corroborate a decline in the number of fatal fires after mid-2012, a t-test is performed.},
  author       = {Hedberg, Jonatan and Lindahl, Elna},
  keyword      = {Poisson-regression,Inhomogen Poisson-process,överspridning,dödsbränder,olycksstatistik,Inhomogenous Poisson-process,overdispersion,fatal fires,accident data},
  language     = {swe},
  note         = {Student Paper},
  title        = {Poisson-modellering av dödsbränder i Sverige},
  year         = {2017},
}