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Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions

Classical distributions such as Burr-G and Weibull-G distributions with less than four parameters are commonly used to represent lifetime data, frequently prove insufficient in accurately describing real observations. These distributions often struggle to capture the complexities and nuances presen...

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Main Author: Nawaz, Shahbaz
Format: Thesis
Language:English
English
English
Published: 2024
Subjects:
QA273-280 Probabilities. Mathematical statistics
Online Access:https://etd.uum.edu.my/11326/1/depositpermission-s903662.pdf
https://etd.uum.edu.my/11326/2/s903622_01.pdf
https://etd.uum.edu.my/11326/3/s903622_02.pdf
https://etd.uum.edu.my/11326/
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spelling my.uum.etd.113262024-10-06T04:22:04Z https://etd.uum.edu.my/11326/ Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions Nawaz, Shahbaz QA273-280 Probabilities. Mathematical statistics Classical distributions such as Burr-G and Weibull-G distributions with less than four parameters are commonly used to represent lifetime data, frequently prove insufficient in accurately describing real observations. These distributions often struggle to capture the complexities and nuances present in the data, leading to inaccuracies in modeling and analysis. Hence, this study introduces two new lifetime models based on the aforementioned distributions to address these issues. These models, called BurrXIIDAL and Weibull-DAL, are based on the properties of the DAL distribution, and have five parameters. Statistical analyses are conducted on these models, including examining their reliability properties and density expansion. Their ordinary and incomplete moments, moment generating function, quantile function, probability weighted moments, order statistics, and Renyi entropy have all been derived explicitly. Maximum likelihood technique is used to provide estimates for the model’s parameter using Iterative Broyden-Flether-Goldfrab-Shanno method in the R-package. Then, five actual datasets are used to demonstrate the ability of the BurrXII-DAL and Weibull- DAL models. Various measures of goodness-of-fit, including AIC, BIC, A*, W* and p-value (KS) are used. Both models, BurrXII-DAL and Weibull-DAL distributions performed better as they are flexible fit to the real data as compared to the other competitive models. The models are proven effective since the prediction of the failure rate is more accurate and the hazard rate function shows flexibility with complicated scenario. BurrXII-DAL and Weibull-DAL distributions with five parameters are successfully developed in this study. This research has provided insights into the strengths and weaknesses of each distribution and has identified situations where one distribution may be more appropriate than the other. 2024 Thesis NonPeerReviewed text en https://etd.uum.edu.my/11326/1/depositpermission-s903662.pdf text en https://etd.uum.edu.my/11326/2/s903622_01.pdf text en https://etd.uum.edu.my/11326/3/s903622_02.pdf Nawaz, Shahbaz (2024) Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions. Doctoral thesis, Universiti Utara Malaysia.
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Electronic Theses
url_provider http://etd.uum.edu.my/
language English
English
English
topic QA273-280 Probabilities. Mathematical statistics
spellingShingle QA273-280 Probabilities. Mathematical statistics
Nawaz, Shahbaz
Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions
description Classical distributions such as Burr-G and Weibull-G distributions with less than four parameters are commonly used to represent lifetime data, frequently prove insufficient in accurately describing real observations. These distributions often struggle to capture the complexities and nuances present in the data, leading to inaccuracies in modeling and analysis. Hence, this study introduces two new lifetime models based on the aforementioned distributions to address these issues. These models, called BurrXIIDAL and Weibull-DAL, are based on the properties of the DAL distribution, and have five parameters. Statistical analyses are conducted on these models, including examining their reliability properties and density expansion. Their ordinary and incomplete moments, moment generating function, quantile function, probability weighted moments, order statistics, and Renyi entropy have all been derived explicitly. Maximum likelihood technique is used to provide estimates for the model’s parameter using Iterative Broyden-Flether-Goldfrab-Shanno method in the R-package. Then, five actual datasets are used to demonstrate the ability of the BurrXII-DAL and Weibull- DAL models. Various measures of goodness-of-fit, including AIC, BIC, A*, W* and p-value (KS) are used. Both models, BurrXII-DAL and Weibull-DAL distributions performed better as they are flexible fit to the real data as compared to the other competitive models. The models are proven effective since the prediction of the failure rate is more accurate and the hazard rate function shows flexibility with complicated scenario. BurrXII-DAL and Weibull-DAL distributions with five parameters are successfully developed in this study. This research has provided insights into the strengths and weaknesses of each distribution and has identified situations where one distribution may be more appropriate than the other.
format Thesis
author Nawaz, Shahbaz
author_facet Nawaz, Shahbaz
author_sort Nawaz, Shahbaz
title Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions
title_short Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions
title_full Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions
title_fullStr Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions
title_full_unstemmed Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions
title_sort modification of dal distribution: a comparative analysis of burr xii-dal and weibull-dal distributions
publishDate 2024
url https://etd.uum.edu.my/11326/1/depositpermission-s903662.pdf
https://etd.uum.edu.my/11326/2/s903622_01.pdf
https://etd.uum.edu.my/11326/3/s903622_02.pdf
https://etd.uum.edu.my/11326/
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score 13.211869

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