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Abstract

This paper introduces a new class of Balakrishnan distribution by extending the multimodal skew-normal distribution proposed by Chakraborty et al. (2015). Statistical properties of the new family of distributions are studied in detail. In particular, explicit expressions of the density and distribution function, moments, skewness, kurtosis and the moments generating function are derived. Furthermore, estimation of the parameters using the maximum likelihood method of the new family of distributions is considered. Finally, the paper ends with an illustration of real-life data sets and then comparing the value of Akaike Information Criterion and Bayesian information criterion of the new distribution with some other known distributions. For the nested models, the Likelihood Ratio Test is carried out.

Keywords

Alpha Skew Distribution Balakrishnan Alpha Skew Normal Distribution Multimodal Skew Normal Distribution Skew Distribution

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How to Cite
SHAH, S., Partha Jyoti Hazarika, Dimpal Pathak, Subrata Chakraborty, & M. Masoom Ali. (2023). The Multimodal Extension of the Balakrishnan Alpha Skew Normal Distribution: Properties and Applications. Pakistan Journal of Statistics and Operation Research, 19(1), 203-217. https://doi.org/10.18187/pjsor.v19i1.4019
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References

  1. Arnold, B. C., and Beaver, R. J. (2000). The skew-Cauchy distribution. Statistics and probability letters, 49(3), 285–290.
  2. Asgharzadeh, A., Esmaeili, L., and Nadarajah, S. (2016). Balakrishnan skew logistic distribution. Communications in Statistics-Theory and Methods, 45(2), 444–464.
  3. Bahrami, W., Agahi, H., and Rangin, H. (2009). A two-parameter Balakrishnan skew-normal distribution. J. Statist. Res. Iran 6, 231–242.
  4. Arnold, B. C., Beaver, R. J., Azzalini, A., Balakrishnan, N., Bhaumik, A., Dey, D. K., and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test, 11, 7-54.
  5. Chakraborty, S., Hazarika, P. J., and Ali, M. M. (2015). A multimodal skewed extension of normal distribution: its properties and applications. Statistics, 49(4), 859–877.
  6. Cook, R., Weisberg, S., (1994). An Introduction to Regression Graphics. John Wiley and Sons, New York.
  7. Elal-Olivero, D. (2010). Alpha-skew-normal distribution. Proyecciones (Antofagasta), 29(3), 224-240.
  8. Fan, S., Gao, P., Zhang, X., Adams, D. J., Kutsop, N. W., Bierson, C. J., and Yung, Y. L. (2022). A bimodal distribution of haze in Pluto’s atmosphere. Nature Communications, 13(1), 240.
  9. Harandi, S. S., and Alamatsaz, M. H. (2013). Alpha–skew–Laplace distribution. Statistics & Probability Letters, 83(3), 774-782.
  10. Hasanalipour, P., and Sharafi, M. (2012). A new generalized Balakrishnan skew-normal distribution. Statistical papers, 53(1), 219–228.
  11. Hazarika, P. J., and Chakraborty, S. (2014). Alpha-skew-logistic distribution. IOSR Journal of Mathematics, 10(4), 36-46.
  12. Hazarika, P. J., Shah, S., and Chakraborty, S. (2020). The Balakrishnan-alpha-skew-normal distribution: properties and applications, Malaysian Journal of Science, 39(2), 71–91.
  13. Huang, W. J., and Chen, Y. H. (2007). Generalized skew-Cauchy distribution. Statistics and probability letters,77(11), 1137–1147.
  14. Mameli, V., and Musio, M. (2013). A generalization of the skew-normal distribution: the beta skew-normal. Communications in Statistics-Theory and methods, 42(12), 2229-2244.
  15. Roeder, K. (1990). Density estimation with confidence sets exemplified by super clusters and voids in the galaxies. Journal of the American Statistical Association, 85(411), 617–624.
  16. Shah, S., Hazarika, P. J., and Chakraborty, S. (2019). The Balakrishnan alpha skew Laplace distribution: Properties and its applications. arXiv preprint arXiv:1910.01084.
  17. Sharafi, M., and Behboodian, J. (2008). The Balakrishnan skew–normal density. Statistical Papers, 49(4), 769–778.
  18. Shafiei, S., Doostparast, M., and Jamalizadeh, A. (2016). The alpha–beta skew normal distribution: Properties and applications. Statistics, 50(2), 338-349.
  19. Sharafi, M., Sajjadnia, Z., and Behboodian, J. (2017). A new generalization of alpha-skew-normal distribution. Communications in Statistics-Theory and Methods, 46(12), 6098-6111.
  20. Torok, A., and Zefreh, M. M. (2016). Assessing the need for applying multimodal speed distribution in road transport macro emission estimation. ActaTechnicaJaurinensis, 9(2), 118–127.
  21. Yadegari, I., Gerami, A., and Khaledi, M. J. (2008). A generalization of the Balakrishnan skew-normal distribution. Statistics and probability letters, 78(10), 1165–1167.