Functional clustering methods and marital fertility modelling
This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnanci...
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Umeå universitet, Institutionen för matematik och matematisk statistik
2017
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ftumeauniv:oai:DiVA.org:umu-130734 2023-10-09T21:54:38+02:00 Functional clustering methods and marital fertility modelling Arnqvist, Per 2017 application/pdf http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130734 eng eng Umeå universitet, Institutionen för matematik och matematisk statistik Umeå : Umeå universitet http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130734 urn:isbn:978-91-7601-669-5 info:eu-repo/semantics/openAccess censoring Coale-Trussell model EM-algorithm functional data analysis functional clustering marital fertility normal approximation Poisson process varved lake sediments warping Probability Theory and Statistics Sannolikhetsteori och statistik Doctoral thesis, comprehensive summary info:eu-repo/semantics/doctoralThesis text 2017 ftumeauniv 2023-09-22T13:50:03Z This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population. The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions. A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent ... Doctoral or Postdoctoral Thesis Northern Sweden Umeå University: Publications (DiVA) |
institution |
Open Polar |
collection |
Umeå University: Publications (DiVA) |
op_collection_id |
ftumeauniv |
language |
English |
topic |
censoring Coale-Trussell model EM-algorithm functional data analysis functional clustering marital fertility normal approximation Poisson process varved lake sediments warping Probability Theory and Statistics Sannolikhetsteori och statistik |
spellingShingle |
censoring Coale-Trussell model EM-algorithm functional data analysis functional clustering marital fertility normal approximation Poisson process varved lake sediments warping Probability Theory and Statistics Sannolikhetsteori och statistik Arnqvist, Per Functional clustering methods and marital fertility modelling |
topic_facet |
censoring Coale-Trussell model EM-algorithm functional data analysis functional clustering marital fertility normal approximation Poisson process varved lake sediments warping Probability Theory and Statistics Sannolikhetsteori och statistik |
description |
This thesis consists of two parts.The first part considers further development of a model used for marital fertility, the Coale-Trussell's fertility model, which is based on age-specific fertility rates. A new model is suggested using individual fertility data and a waiting time after pregnancies. The model is named the waiting model and can be understood as an alternating renewal process with age-specific intensities. Due to the complicated form of the waiting model and the way data is presented, as given in the United Nation Demographic Year Book 1965, a normal approximation is suggested together with a normal approximation of the mean and variance of the number of births per summarized interval. A further refinement of the model was then introduced to allow for left truncated and censored individual data, summarized as table data. The waiting model suggested gives better understanding of marital fertility and by a simulation study it is shown that the waiting model outperforms the Coale-Trussell model when it comes to estimating the fertility intensity and to predict the mean and variance of the number of births for a population. The second part of the thesis focus on developing functional clustering methods.The methods are motivated by and applied to varved (annually laminated) sediment data from lake Kassj\"on in northern Sweden. The rich but complex information (with respect to climate) in the varves, including the shapes of the seasonal patterns, the varying varve thickness, and the non-linear sediment accumulation rates makes it non-trivial to cluster the varves. Functional representations, smoothing and alignment are functional data tools used to make the seasonal patterns comparable.Functional clustering is used to group the seasonal patterns into different types, which can be associated with different weather conditions. A new non-parametric functional clustering method is suggested, the Bagging Voronoi K-mediod Alignment algorithm, (BVKMA), which simultaneously clusters and aligns spatially dependent ... |
format |
Doctoral or Postdoctoral Thesis |
author |
Arnqvist, Per |
author_facet |
Arnqvist, Per |
author_sort |
Arnqvist, Per |
title |
Functional clustering methods and marital fertility modelling |
title_short |
Functional clustering methods and marital fertility modelling |
title_full |
Functional clustering methods and marital fertility modelling |
title_fullStr |
Functional clustering methods and marital fertility modelling |
title_full_unstemmed |
Functional clustering methods and marital fertility modelling |
title_sort |
functional clustering methods and marital fertility modelling |
publisher |
Umeå universitet, Institutionen för matematik och matematisk statistik |
publishDate |
2017 |
url |
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130734 |
genre |
Northern Sweden |
genre_facet |
Northern Sweden |
op_relation |
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130734 urn:isbn:978-91-7601-669-5 |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1779318295516676096 |