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https://ptsldigital.ukm.my/jspui/handle/123456789/499791Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Noriszura Ismail, Dr. | |
| dc.contributor.author | Faroughi Pouya (P64543) | |
| dc.date.accessioned | 2023-10-13T09:34:45Z | - |
| dc.date.available | 2023-10-13T09:34:45Z | - |
| dc.date.issued | 2015-12-08 | |
| dc.identifier.other | ukmvital:83066 | |
| dc.identifier.uri | https://ptsldigital.ukm.my/jspui/handle/123456789/499791 | - |
| dc.description | Bivariate Poisson (BP) distribution is a standard distribution for modeling bivariate count data without covariates. Mixed distribution is an important approach for obtaining a new probability distribution which provides a more flexible alternative than BP distribution. This study suggests a new bivariate Poisson-weighted exponential (BPWE) distribution for modeling dependent and overdispersed count data without covariates. The BPWE distribution is obtained by mixing a Poisson distribution with a weighted exponential distribution. There are many forms of bivariate discrete distribution where several forms are derived from the method of trivariate reduction. However, all of the bivariate distributions derived from trivariate reduction consider only non-negative correlation. This study applies bivariate Poisson-Lindley (BPL) distribution for modeling dependent and overdispersed count data without covariates where the correlation can be positive or negative. The BPL distribution is derived from the product of two Poisson-Lindley marginals with a multiplicative factor parameter. Several bivariate regression models such as BP, bivariate negative binomial (BNB) and bivariate generalized Poisson (BGP) have been fitted for modeling under- or overdispersed bivariate count data with covariates. However, these regression models are not nested and likelihood ratio test (LRT) cannot be performed to choose a better model. This study proposes several new forms of BGP and BNB regression models which are nested, allow LRT for choosing the best model, have positive, zero or negative correlation, can be used for fitting over- or underdispersed response variables, and have flexible form of marginal mean-variance relationships. The new models are derived from the product of two generalized Poisson (or negative binomial) marginals and a mulitiplicative factor parameter. Bivariate count data often display excessive number of zero outcomes than are expected in BP regression model. The bivariate zero-inflated Poisson (BZIP) regression model has been considered for purely zero-inflated bivariate count data with covariates. In this study, we suggest several new forms of bivariate zero-inflated negative binomial (BZINB) and bivariate zero-inflated generalized Poisson (BZIGP) regression models which are nested, allow LRT for choosing the best model, can be used for zero-inflated data, have flexible forms of marginal mean-variance relationships, and have positive or negative correlation. The new models are derived from mixing a distribution degenerate at zero with a BNB (or BGP) distribution where the explanatory variables are incorporated in both the zero process and the BNB (or BGP) distribution. In this study, the new distributions and regression models are fitted to real datasets from several areas; accident, flights, healthcare (Australia and US) and insurance (Malaysia). This thesis has six main contributions. The first contribution is the proposal of a new BPWE distribution for modeling dependent and overdispersed bivariate count data with positive correlation. The second contribution is the application of BPL distribution for modeling dependent and overdispersed bivariate count data with positive, zero or negative correlation. The third and fourth contributions are the suggestion of several new forms of BGP and BNB regression models for fitting over- or underdispersed bivariate count data with covariates where the correlation can be positive, zero or negative. Finally, the fifth and sixth contributions are the proposal of several new forms of BZIGP and BZINB regression models for modelling bivariate zero-inflated count data with covariates where the correlation can be positive or negative.,Ph.D,Taburan bivariat Poisson (BP) adalah taburan piawai untuk pemodelan data bilangan bivariat tanpa kovariat. Taburan campuran merupakan pendekatan penting untuk memperoleh suatu taburan kebarangkalian baru yang memberikan alternatif lebih fleksibel daripada taburan BP. Kajian ini mencadang taburan baru bivariat Poisson-eksponen berpemberat (BPWE) untuk pemodelan data bilangan tanpa kovariat yang bersandar dan terlebih-serak. Taburan ini diperoleh melalui campuran taburan Poisson dengan taburan eksponen berpemberat. Terdapat banyak bentuk taburan diskret bivariat yang beberapa daripadanya diperoleh daripada kaedah pengurangan trivariat. Namun, semua taburan bivariat yang diperoleh daripada kaedah ini hanya mempertimbangkan kolerasi bukan-negatif. Kajian ini menggunakan taburan bivariat Poisson-Lindley (BPL) untuk memodelkan data bilangan tanpa kovariat yang bersandar, terlebih-serak, dan berkolerasi positif atau negatif. Taburan ini diperoleh daripada hasildarab dua marginal Poisson-Lindley dengan parameter faktor pendaraban. Beberapa model regresi seperti BP, bivariat binomial negatif (BNB) dan bivariat Poisson teritlak (BGP) telah disuai untuk memodelkan data bilangan bivariat dengan kovariat yang terkurang- atau terlebih-serak. Namun, model-model regresi ini tidak tersarang dan ujian nisbah kebolehjadian (LRT) tidak boleh dilakukan untuk memilih model yang lebih baik. Kajian ini mengusul beberapa bentuk berfungsi baru bagi model regresi BGP dan BNB yang tersarang, membenarkan LRT untuk memilih model terbaik, berkolerasi positif atau negatif, boleh diguna untuk menyuai pemboleh ubah respons yang terlebih- atau terkurang-serak, dan mempunyai bentuk fleksibel untuk hubungan marginal min-varians. Model-model baru ini diperoleh daripada hasildarab dua marginal Poisson teritlak (atau binomial negatif) dengan parameter faktor pendaraban. Data bilangan bivariat sering menunjukkan bilangan sifar yang berlebihan daripada nilai jangkaan model regresi BP. Model regresi bivariat inflasi-sifar Poisson (BZIP) telah dipertimbangkan untuk data bilangan bivariat dengan kovariat bagi inflasi-sifar yang tulen. Dalam kajian ini, kami mencadang beberapa bentuk baru bagi model regresi bivariat inflasi-sifar binomial negatif (BZINB) dan bivariat inflasi-sifar Poisson teritlak (BZIGP) yang tersarang, membenarkan LRT untuk memilih model terbaik, mempunyai bentuk fleksibel untuk hubungan marginal min-varians, dan berkolerasi positif atau negatif. Model-model baru ini diperoleh dengan mencampurkan suatu taburan merosot pada sifar dengan suatu taburan BNB (atau BGP), dan memasukkan pemboleh ubah penerang dalam kedua-dua proses sifar dan taburan BNB (atau BGP). Dalam kajian ini, taburan dan model regresi baru disuai kepada set data sebenar dari beberapa bidang; kemalangan, penerbangan, penjagaan kesihatan (US dan Australia) dan insurans (Malaysia). Tesis ini mempunyai enam sumbangan utama. Sumbangan pertama adalah cadangan taburan baru BPWE untuk memodelkan data bilangan bivariat yang terlebih-serak dan berkolerasi positif. Sumbangan kedua adalah penggunaan taburan BPL untuk pemodelan data bilangan bivariat yang terlebih-serak dan berkolerasi positif, sifar atau negatif. Sumbangan ketiga dan keempat adalah cadangan beberapa model regresi baru BGP and BNB untuk penyuaian data bilangan bivariat dengan kovariat yang terlebih- atau terkurang-serak dan berkolerasi positif, sifar atau negatif. Akhir sekali, sumbangan kelima dan keenam adalah cadangan beberapa model regresi baru BZIGP and BZINB untuk pemodelan data bilangan bivariat inflasi-sifar dengan kovariat yang berkolerasi positif atau negatif. | |
| dc.language.iso | eng | |
| dc.publisher | UKM, Bangi | |
| dc.relation | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
| dc.rights | UKM | |
| dc.subject | Poisson distribution | |
| dc.subject | Distribution (Probability theory) | |
| dc.title | Several new bivariate models for count data with applications | |
| dc.type | Theses | |
| dc.format.pages | 211 | |
| dc.identifier.callno | QA273.6.F346 2015 | |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi | |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| ukmvital_83066+SOURCE1+SOURCE1.0.PDF Restricted Access | 3.09 MB | Adobe PDF |  View/Open |
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