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A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros

Count data often exhibits the property of dispersion and have large number of zeros. In order to take these properties into account, a new generalized negative binomial-Lindley distribution with four parameters is proposed, of which the two-parameter and three-parameter negative binomial-Lindley dis...

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Main Authors: Tajuddin, Razik Ridzuan Mohd, Ismail, Noriszura, Ibrahim, Kamarulzaman, Abu Bakar, Shaiful Anuar
Format: Article
Published: Taylor & Francis 2022
Subjects:
QA Mathematics
Online Access:http://eprints.um.edu.my/33872/
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spelling my.um.eprints.338722022-04-22T07:22:59Z http://eprints.um.edu.my/33872/ A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros Tajuddin, Razik Ridzuan Mohd Ismail, Noriszura Ibrahim, Kamarulzaman Abu Bakar, Shaiful Anuar QA Mathematics Count data often exhibits the property of dispersion and have large number of zeros. In order to take these properties into account, a new generalized negative binomial-Lindley distribution with four parameters is proposed, of which the two-parameter and three-parameter negative binomial-Lindley distributions are special cases. Several statistical properties of the proposed distribution are presented. The dispersion index for the proposed distribution is derived and based on the index, it is clear that the proposed distribution can adequately fit the data with properties of overdispersion or underdispersion depending on the choice of the parameters. The proposed distribution is fitted to three overdispersed datasets with large proportion of zeros. The best fitted model is selected based on the values of AIC, mean absolute error and root mean squared error. From the model fittings, it can be concluded that the proposed distribution outperforms Poisson and negative binomial distributions in fitting the count data with overdispersion and large number of zeros. Taylor & Francis 2022-01-17 Article PeerReviewed Tajuddin, Razik Ridzuan Mohd and Ismail, Noriszura and Ibrahim, Kamarulzaman and Abu Bakar, Shaiful Anuar (2022) A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros. Communications in Statistics - Theory and Methods, 51 (2). pp. 414-426. ISSN 0361-0926, DOI https://doi.org/10.1080/03610926.2020.1749854 <https://doi.org/10.1080/03610926.2020.1749854>. 10.1080/03610926.2020.1749854
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Tajuddin, Razik Ridzuan Mohd
Ismail, Noriszura
Ibrahim, Kamarulzaman
Abu Bakar, Shaiful Anuar
A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros
description Count data often exhibits the property of dispersion and have large number of zeros. In order to take these properties into account, a new generalized negative binomial-Lindley distribution with four parameters is proposed, of which the two-parameter and three-parameter negative binomial-Lindley distributions are special cases. Several statistical properties of the proposed distribution are presented. The dispersion index for the proposed distribution is derived and based on the index, it is clear that the proposed distribution can adequately fit the data with properties of overdispersion or underdispersion depending on the choice of the parameters. The proposed distribution is fitted to three overdispersed datasets with large proportion of zeros. The best fitted model is selected based on the values of AIC, mean absolute error and root mean squared error. From the model fittings, it can be concluded that the proposed distribution outperforms Poisson and negative binomial distributions in fitting the count data with overdispersion and large number of zeros.
format Article
author Tajuddin, Razik Ridzuan Mohd
Ismail, Noriszura
Ibrahim, Kamarulzaman
Abu Bakar, Shaiful Anuar
author_facet Tajuddin, Razik Ridzuan Mohd
Ismail, Noriszura
Ibrahim, Kamarulzaman
Abu Bakar, Shaiful Anuar
author_sort Tajuddin, Razik Ridzuan Mohd
title A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros
title_short A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros
title_full A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros
title_fullStr A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros
title_full_unstemmed A four-parameter negative binomial-Lindley distribution for modeling over and underdispersed count data with excess zeros
title_sort four-parameter negative binomial-lindley distribution for modeling over and underdispersed count data with excess zeros
publisher Taylor & Francis
publishDate 2022
url http://eprints.um.edu.my/33872/
_version_ 1735409602314371072
score 13.211869

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