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A new zero-inflated regression model with application

Year 2018, Volume: 11 Issue: 2, 73 - 80, 31.12.2018

Abstract

 In this paper, a new zero-inflated regression model, called Zero-Inflated Poisson-Lindley regression model, is proposed for count data modeling. Poisson-Lindley distribution arises from the Poisson distribution when its parameter follows a Lindley distribution. Contrary to Poisson distribution, Poisson-Lindley distribution allows for over-dispersion. Therefore, a new model is good candidate to model the over-dispersed and zero-inflated data sets. Application of proposed model to real data set is given and compared with Poisson and Zero-Inflated Poisson regression models. Empirical findings reveal that the Zero-Inflated Poisson-Lindley regression model provides better fits than Zero-Inflated Poisson regression model for zero-inflated and over-dispersed data set.


References

  • [1] M. Sankaran, 1970, The Discrete Poisson-Lindley Distribution, Biometrics, 145-149.
  • [2] M. Denuit, X. Maréchal, S. Pitrebois, J. F. Walhin, 2007, Actuarial modelling of claim counts: Risk classification, credibility and bonus-malus systems, John Wiley & Sons.
  • [3] E. Avcı, S. Alturk, E. N. Soylu, E, 2015, Comparison count regression models for overdispersed alga data, IJRRAS, 25(1), 1-5.
  • [4] N. Ismail, H. Zamani, 2013, Estimation of claim count data using negative binomial, generalized Poisson, zero-inflated negative binomial and zero-inflated generalized Poisson regression models, In Casualty Actuarial Society E-Forum, 41(20),1-18.
  • [5] D. Lord, S.P. Washington, J.N. Ivan, 2005, Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory, Accident Analysis and Prevention, 37, 35-46.
  • [6] E. Ayati, E.Abbasi, 2014, Modeling Accidents on Mashhad Urban Highways, Open Journal of Safety Science and Technology, 4, 22-35.
  • [7] D. Xavier, M. Santos-Neto, M. Bourguignon, V. Tomazella, 2017, Zero-Modified Poisson-Lindley distribution with applications in zero-inflated and zero-deflated count data. arXiv preprint arXiv:1712.04088.
  • [8] J. Van den Broek, 1995, A score test for zero inflation in a Poisson distribution. Biometrics, 738-743.

Yeni sıfır yığılmalı regresyon modeli ve uygulaması

Year 2018, Volume: 11 Issue: 2, 73 - 80, 31.12.2018

Abstract

Bu çalışmada, sayım verilerinin modellenmesi için sıfır yığılmalı Poisson-Lindley regresyon modeli olarak adlandırılan yeni bir sıfır yığılmalı regresyon modeli önerilmiştir. Poisson-Lindley dağılımı, Poisson dağılımının parameteresinin Lindley dağılımına sahip olduğu durumda ortaya çıkmaktadır. Poisson dağılımının aksine, Poisson-Lindley dağılımı aşırı yayılıma izin verir. Bu nedenle, yeni model aşırı yayılımlı ve sıfır yığılmalı veri kümelerini modellemek için iyi bir seçenektir. Önerilen modelin gerçek veri seti üzerine uygulaması verilmiş, Poisson ve Zero-Inflated Poisson regresyon modelleriyle karşılaştırılmıştır. Elde edilen bulgular, sıfır yığılmalı Poisson-Lindley regresyon modelinin, sıfır yığılmalı ve aşırı yayılım gösteren veri seti için, sıfır yığılmalı Poisson regresyon modelinden daha iyi uyum sağladığını göstermektedir.

References

  • [1] M. Sankaran, 1970, The Discrete Poisson-Lindley Distribution, Biometrics, 145-149.
  • [2] M. Denuit, X. Maréchal, S. Pitrebois, J. F. Walhin, 2007, Actuarial modelling of claim counts: Risk classification, credibility and bonus-malus systems, John Wiley & Sons.
  • [3] E. Avcı, S. Alturk, E. N. Soylu, E, 2015, Comparison count regression models for overdispersed alga data, IJRRAS, 25(1), 1-5.
  • [4] N. Ismail, H. Zamani, 2013, Estimation of claim count data using negative binomial, generalized Poisson, zero-inflated negative binomial and zero-inflated generalized Poisson regression models, In Casualty Actuarial Society E-Forum, 41(20),1-18.
  • [5] D. Lord, S.P. Washington, J.N. Ivan, 2005, Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory, Accident Analysis and Prevention, 37, 35-46.
  • [6] E. Ayati, E.Abbasi, 2014, Modeling Accidents on Mashhad Urban Highways, Open Journal of Safety Science and Technology, 4, 22-35.
  • [7] D. Xavier, M. Santos-Neto, M. Bourguignon, V. Tomazella, 2017, Zero-Modified Poisson-Lindley distribution with applications in zero-inflated and zero-deflated count data. arXiv preprint arXiv:1712.04088.
  • [8] J. Van den Broek, 1995, A score test for zero inflation in a Poisson distribution. Biometrics, 738-743.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Emrah Altun 0000-0001-5065-2523

Publication Date December 31, 2018
Published in Issue Year 2018 Volume: 11 Issue: 2

Cite

IEEE E. Altun, “A new zero-inflated regression model with application”, JSSA, vol. 11, no. 2, pp. 73–80, 2018.