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...

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Bibliographic Details
Published in:PloS one Vol. 17; no. 5; p. e0261901
Main Authors: Iftikhar, Ayesha, Ali, Azeem, Hanif, Muhammad
Format: Journal Article
Language:English
Published: United States Public Library of Science 17.05.2022
Public Library of Science (PLoS)
Subjects:
Analysis
Arithmetic
Biology and Life Sciences
Cornea
Data analysis
Data mining
Evaluation
Humans
Mathematical models
Maximum likelihood estimation
Medicine and Health Sciences
Monte Carlo Method
Monte Carlo simulation
Parameter estimation
Parameters
Physical Sciences
Research and Analysis Methods
Research Design
Skewness
Pakistan
ISSN:1932-6203, 1932-6203
Online Access:Get full text
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Summary: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.
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Current address: The University of Lahore, Lahore, Pakistan
Competing Interests: The author(s) received no specific funding for this work.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0261901