Half circular modified burr-III distribution, application with different estimation methods
The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in s...
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| Veröffentlicht in: | PloS one 2022-05, Vol.17 (5), p.e0261901-e0261901 |
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| creator | Iftikhar, Ayesha Ali, Azeem Hanif, Muhammad |
| description | The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr-III distribution, called the half circular modified Burr-III (hcMB-III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB-III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. Finally, one data set related to posterior corneal curvature of the eyes of 23 patients, is analyzed to check potentiality of the newly proposed model. |
| doi_str_mv | 10.1371/journal.pone.0261901 |
| format | Article |
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This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr-III distribution, called the half circular modified Burr-III (hcMB-III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB-III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. Finally, one data set related to posterior corneal curvature of the eyes of 23 patients, is analyzed to check potentiality of the newly proposed model.</description><identifier>ISSN: 1932-6203</identifier><identifier>EISSN: 1932-6203</identifier><identifier>DOI: 10.1371/journal.pone.0261901</identifier><identifier>PMID: 35580119</identifier><language>eng</language><publisher>United States: Public Library of Science</publisher><subject>Analysis ; Arithmetic ; Biology and Life Sciences ; Cornea ; Data analysis ; Data mining ; Evaluation ; Mathematical models ; Maximum likelihood estimation ; Medicine and Health Sciences ; Monte Carlo simulation ; Parameter estimation ; Parameters ; Physical Sciences ; Research and Analysis Methods ; Skewness</subject><ispartof>PloS one, 2022-05, Vol.17 (5), p.e0261901-e0261901</ispartof><rights>COPYRIGHT 2022 Public Library of Science</rights><rights>2022 Iftikhar et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 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This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr-III distribution, called the half circular modified Burr-III (hcMB-III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB-III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. 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circular modified burr-III distribution, application with different estimation methods</atitle><jtitle>PloS one</jtitle><addtitle>PLoS One</addtitle><date>2022-05-17</date><risdate>2022</risdate><volume>17</volume><issue>5</issue><spage>e0261901</spage><epage>e0261901</epage><pages>e0261901-e0261901</pages><issn>1932-6203</issn><eissn>1932-6203</eissn><abstract>The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr-III distribution, called the half circular modified Burr-III (hcMB-III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB-III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. 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| subjects | Analysis Arithmetic Biology and Life Sciences Cornea Data analysis Data mining Evaluation Mathematical models Maximum likelihood estimation Medicine and Health Sciences Monte Carlo simulation Parameter estimation Parameters Physical Sciences Research and Analysis Methods Skewness |
| title | Half circular modified burr-III distribution, application with different estimation methods |
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