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Year 2021, Volume: 50 Issue: 2, 559 - 578, 11.04.2021

Hassan Bakouch Christophe Chesneau Kadir Karakaya Coşkun Kuş

https://doi.org/10.15672/hujms.740872
Cited By: 8

Abstract

References

  • [1] Y. Akdoğan, C. Kuş, A. Asgharzadeh, İ. Kınacı and F. Sharafi, Uniform-geometric distribution, J. Stat. Comput. Simul. 86 (9), 1754-1774, 2016.
  • [2] A. Atkinson, Two graphical displays for outlying and influential observations in regression, Biometrika 68 (1), 13-20, 1981.
  • [3] H.S. Bakouch, A weighted negative binomial Lindley distribution with applications to dispersed data, An. Acad. Brasil. Ciênc. 90 (3), 2617-2642, 2018.
  • [4] D. Bhati and S. Joshi, Weighted geometric distribution with a new characterization of geometric distribution, Comm. Statist. Theory Methods 47 (6), 1510-1527, 2018.
  • [5] A.C. Cameron, P.K. Trivedi, F. Milne and J. Piggott, A microeconomic model of the demand for health care and health insurance in Australia, Rev. Econ. Stud. 55 (1), 85-106, 1988.
  • [6] J.D. Castillo and M.P. Casany, Weighted Poisson Distributions and under dispersion Situations, Ann. Inst. Statist. Math. 5, 567-585, 1998.
  • [7] C. Chesneau, H.S. Bakouch, T. Hussain and B.A. Para, The cosine geometric distribution with count data modeling, J. Appl. Stat. 48 (1), 124-137, 2021.
  • [8] D.A.S. Fraser, Probability and Statistics: Theory and Applications, North Scituate MA, Duxbury Press, 1976.
  • [9] M.G. Kendall, Natural law in social sciences, J. Roy. Statist. Soc. Ser. A 124, 1-19, 1961.
  • [10] M.S.A. Khan, A. Khalique and A.M. Abouammoh, On estimating parameters in a discrete, Weibull distribution, IEEE Trans. Reliab. 38 (3), 348-350, 1989.
  • [11] C. Kuş, Y. Akdoğan, A. Asgharzadeh, İ. Kınacı and K. Karakaya, Binomial-discrete Lindley distribution, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 68 (1), 401-411, 2018.
  • [12] A.J. Lemonte, G. Moreno-Arenas and F. Castellares, Zero inflated Bell regression models for count data, J. Appl. Stat. 47 (2), 265-286, 2020.
  • [13] G.P. Patil and C.R. Rao, The weighted distributions: A survey and their applications, in: Krishnaiah, P.R. (ed.) Applications of statistics, North-Holland Publ. Co., Amsterdam, 1977.
  • [14] G.P. Patil and C.R. Rao, Weighted distributions and size biased sampling with applications to wild-life populations and human families, Biometrica 34, 179-189, 1978.
  • [15] C.R. Rao, On discrete distributions arising out of methods of ascertainment, Sankhya A, 311-324, 1965.

The Cos-Poisson model with a novel count regression analysis

Year 2021, Volume: 50 Issue: 2, 559 - 578, 11.04.2021

Hassan Bakouch Christophe Chesneau Kadir Karakaya Coşkun Kuş

https://doi.org/10.15672/hujms.740872
Cited By: 8

Abstract

In this paper, we propose a new generalization of the Poisson distribution by using the concept of the weighted distribution; a trigonometric weight with the cosine function is used. We derive some distributional properties of the new distribution, such as the cumulative distribution function, moment generating function, factorial moments, and index of dispersion. Then, the related model is considered for modeling purposes, with estimation of the model parameters performed via several methods. Zero-inflated count regression analysis is introduced by using the new distribution. Finally, we provide two applications of the obtained results on practical data sets.

Keywords

confidence interval count data count regression index of dispersion zero-inflated data

References

  • [1] Y. Akdoğan, C. Kuş, A. Asgharzadeh, İ. Kınacı and F. Sharafi, Uniform-geometric distribution, J. Stat. Comput. Simul. 86 (9), 1754-1774, 2016.
  • [2] A. Atkinson, Two graphical displays for outlying and influential observations in regression, Biometrika 68 (1), 13-20, 1981.
  • [3] H.S. Bakouch, A weighted negative binomial Lindley distribution with applications to dispersed data, An. Acad. Brasil. Ciênc. 90 (3), 2617-2642, 2018.
  • [4] D. Bhati and S. Joshi, Weighted geometric distribution with a new characterization of geometric distribution, Comm. Statist. Theory Methods 47 (6), 1510-1527, 2018.
  • [5] A.C. Cameron, P.K. Trivedi, F. Milne and J. Piggott, A microeconomic model of the demand for health care and health insurance in Australia, Rev. Econ. Stud. 55 (1), 85-106, 1988.
  • [6] J.D. Castillo and M.P. Casany, Weighted Poisson Distributions and under dispersion Situations, Ann. Inst. Statist. Math. 5, 567-585, 1998.
  • [7] C. Chesneau, H.S. Bakouch, T. Hussain and B.A. Para, The cosine geometric distribution with count data modeling, J. Appl. Stat. 48 (1), 124-137, 2021.
  • [8] D.A.S. Fraser, Probability and Statistics: Theory and Applications, North Scituate MA, Duxbury Press, 1976.
  • [9] M.G. Kendall, Natural law in social sciences, J. Roy. Statist. Soc. Ser. A 124, 1-19, 1961.
  • [10] M.S.A. Khan, A. Khalique and A.M. Abouammoh, On estimating parameters in a discrete, Weibull distribution, IEEE Trans. Reliab. 38 (3), 348-350, 1989.
  • [11] C. Kuş, Y. Akdoğan, A. Asgharzadeh, İ. Kınacı and K. Karakaya, Binomial-discrete Lindley distribution, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 68 (1), 401-411, 2018.
  • [12] A.J. Lemonte, G. Moreno-Arenas and F. Castellares, Zero inflated Bell regression models for count data, J. Appl. Stat. 47 (2), 265-286, 2020.
  • [13] G.P. Patil and C.R. Rao, The weighted distributions: A survey and their applications, in: Krishnaiah, P.R. (ed.) Applications of statistics, North-Holland Publ. Co., Amsterdam, 1977.
  • [14] G.P. Patil and C.R. Rao, Weighted distributions and size biased sampling with applications to wild-life populations and human families, Biometrica 34, 179-189, 1978.
  • [15] C.R. Rao, On discrete distributions arising out of methods of ascertainment, Sankhya A, 311-324, 1965.
There are 15 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Hassan Bakouch 0000-0002-3189-0670

Christophe Chesneau 0000-0002-1522-9292

Kadir Karakaya 0000-0002-0781-3587

Coşkun Kuş 0000-0002-7176-0176

Publication Date April 11, 2021
Published in Issue Year 2021 Volume: 50 Issue: 2

Cite

APA Bakouch, H., Chesneau, C., Karakaya, K., Kuş, C. (2021). The Cos-Poisson model with a novel count regression analysis. Hacettepe Journal of Mathematics and Statistics, 50(2), 559-578. https://doi.org/10.15672/hujms.740872
AMA Bakouch H, Chesneau C, Karakaya K, Kuş C. The Cos-Poisson model with a novel count regression analysis. Hacettepe Journal of Mathematics and Statistics. April 2021;50(2):559-578. doi:10.15672/hujms.740872
Chicago Bakouch, Hassan, Christophe Chesneau, Kadir Karakaya, and Coşkun Kuş. “The Cos-Poisson Model With a Novel Count Regression Analysis”. Hacettepe Journal of Mathematics and Statistics 50, no. 2 (April 2021): 559-78. https://doi.org/10.15672/hujms.740872.
EndNote Bakouch H, Chesneau C, Karakaya K, Kuş C (April 1, 2021) The Cos-Poisson model with a novel count regression analysis. Hacettepe Journal of Mathematics and Statistics 50 2 559–578.
IEEE H. Bakouch, C. Chesneau, K. Karakaya, and C. Kuş, “The Cos-Poisson model with a novel count regression analysis”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, pp. 559–578, 2021, doi: 10.15672/hujms.740872.
ISNAD Bakouch, Hassan et al. “The Cos-Poisson Model With a Novel Count Regression Analysis”. Hacettepe Journal of Mathematics and Statistics 50/2 (April 2021), 559-578. https://doi.org/10.15672/hujms.740872.
JAMA Bakouch H, Chesneau C, Karakaya K, Kuş C. The Cos-Poisson model with a novel count regression analysis. Hacettepe Journal of Mathematics and Statistics. 2021;50:559–578.
MLA Bakouch, Hassan et al. “The Cos-Poisson Model With a Novel Count Regression Analysis”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, 2021, pp. 559-78, doi:10.15672/hujms.740872.
Vancouver Bakouch H, Chesneau C, Karakaya K, Kuş C. The Cos-Poisson model with a novel count regression analysis. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):559-78.

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