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Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data

The one-inflated positive Poisson Lindley model has been recently introduced as an alternative in modelling positive count data with a large number of ones: a phenomenon known as one-inflation. In the presence of oneinflation, this model has a high tendency to be influenced by outliers, making usual...

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Main Authors: Mohd Tajuddin, Razik Ridzuan, Mohd Safari, Muhammad Aslam, Ismail, Noriszura
Format: Article
Language:English
Published: University of Punjab 2024
Online Access:http://psasir.upm.edu.my/id/eprint/114966/1/114966.pdf
http://psasir.upm.edu.my/id/eprint/114966/
https://pjsor.com/pjsor/article/view/4538
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spelling my.upm.eprints.1149662025-02-13T03:28:39Z http://psasir.upm.edu.my/id/eprint/114966/ Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data Mohd Tajuddin, Razik Ridzuan Mohd Safari, Muhammad Aslam Ismail, Noriszura The one-inflated positive Poisson Lindley model has been recently introduced as an alternative in modelling positive count data with a large number of ones: a phenomenon known as one-inflation. In the presence of oneinflation, this model has a high tendency to be influenced by outliers, making usual parameter estimations to be less robust. Hence, several estimators: maximum likelihood, method of moments, ordinary least squares, weighted least squares, Cramér-Von Mises, modified Cramér-Von Mises (MCVM) and maximum product of spacing (MPS); for the parameters of the model are also proposed and investigated in terms of unbiasedness, consistency and joint efficiency under the presence and absence of outliers. When the outliers are absent, the MPS estimator is the best estimator and when the outliers are present, the MCVM estimator is the best estimator. Model fittings to two real datasets with one-inflation and outliers support the simulation results and conclude that the MCVM estimator is the best estimator. Based on the best robust estimator, the population size of the number of offenders as well as the likelihood of arrests were estimated. University of Punjab 2024-09-07 Article PeerReviewed text en cc_by_4 http://psasir.upm.edu.my/id/eprint/114966/1/114966.pdf Mohd Tajuddin, Razik Ridzuan and Mohd Safari, Muhammad Aslam and Ismail, Noriszura (2024) Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data. Pakistan Journal of Statistics and Operation Research, 20 (3). pp. 369-381. ISSN 1816-2711; eISSN: 2220-5810 https://pjsor.com/pjsor/article/view/4538 10.18187/pjsor.v20i3.4538
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description The one-inflated positive Poisson Lindley model has been recently introduced as an alternative in modelling positive count data with a large number of ones: a phenomenon known as one-inflation. In the presence of oneinflation, this model has a high tendency to be influenced by outliers, making usual parameter estimations to be less robust. Hence, several estimators: maximum likelihood, method of moments, ordinary least squares, weighted least squares, Cramér-Von Mises, modified Cramér-Von Mises (MCVM) and maximum product of spacing (MPS); for the parameters of the model are also proposed and investigated in terms of unbiasedness, consistency and joint efficiency under the presence and absence of outliers. When the outliers are absent, the MPS estimator is the best estimator and when the outliers are present, the MCVM estimator is the best estimator. Model fittings to two real datasets with one-inflation and outliers support the simulation results and conclude that the MCVM estimator is the best estimator. Based on the best robust estimator, the population size of the number of offenders as well as the likelihood of arrests were estimated.
format Article
author Mohd Tajuddin, Razik Ridzuan
Mohd Safari, Muhammad Aslam
Ismail, Noriszura
spellingShingle Mohd Tajuddin, Razik Ridzuan
Mohd Safari, Muhammad Aslam
Ismail, Noriszura
Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
author_facet Mohd Tajuddin, Razik Ridzuan
Mohd Safari, Muhammad Aslam
Ismail, Noriszura
author_sort Mohd Tajuddin, Razik Ridzuan
title Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
title_short Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
title_full Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
title_fullStr Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
title_full_unstemmed Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
title_sort robust parameter estimation for one-inflated positive poisson lindley distribution under the presence and absence of outliers with applications to crime data
publisher University of Punjab
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/114966/1/114966.pdf
http://psasir.upm.edu.my/id/eprint/114966/
https://pjsor.com/pjsor/article/view/4538
_version_ 1825162406742982656
score 13.244413

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