TARU PUBLICATIONS
Journal of Statistics and Management Systems cover

Journal of Statistics and Management Systems

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510
Powered by:Powered by

The Journal of Statistics and Management Systems (JSMS) is a world leading journal publishing high quality, rigorously peer-reviewed original research on theoretical and applied statistics and management systems since 1998. The scope is intentionally broad, but papers must make a novel contribution to the field to be considered for publication. Topics include, but are not limited to, the following: • Statistics • Applied Statistics • Industrial Statistics • Statistical Inference • Interdisciplinary role of Statistics • Actuarial Sciences • Decision Sciences • Managerial Aspects • Management Sciences • Management Information Systems

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Taru Online First Current IssueSpecial IssuesBrowse all Issues
Journal of Statistics and Management Systems
Open Access Research Article

A generalization of Balakrishnan-alpha-skew-normal distribution : Properties, characterisations and applications

, * , ,

* Corresponding author · click or hover a name for details

pp. 9–33Vol. 27Issue 1January 2024DOI: 10.47974/JSMS-1013XML
Received:
05 Apr 2022
Accepted:
10 Aug 2022
Published Online:
08 Jan 2024
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1013
Pages:
9–33

Abstract

In this article, a generalized form of the Balakrishnan-alpha-skew-normal distribution of Hazarika et al. (2020) is proposed and some of its simple and distributional properties are studied. Two characterizations have also been presented. For model selection criteria namely Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), are used to check appropriateness of the proposed distribution by conducting data fitting experiments and comparing it with some other related distributions. The likelihood ratio test is employed for discriminating between nested models.

Keywords

Skew distributionBimodal distributionAlpha-skew-normal distributionBalakrishnan-alpha-skew-normal distributionAICBIC

Subject Classifications

60E0562H1062H12

References

[1] Arnold, B. C., and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test, 11(1), 7-54.
[2] Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171-178.
[3] Bahrami,W., Agahi, H., and Rangin, H. (2009). A Two-Parameter Balakrishnan Skew-Normal Distribution,  J. Statist. Res. Iran, 6, 231–242.
[4] Balakrishnan, N. (2002). Discussion on “Skew multivariate models related to hidden truncation and/or selective reporting” by B. C. Arnold and R. J. Beaver. Test 11, 37-39
[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.D.,  and Weisberg, S. (1994). An Introduction to Regression Analysis, Wiley, New York. 
[7] Elal-Olivero, D. (2010). Alpha-skew-normal distribution.  Proyecciones (Antofagasta), 29 (3), 224-240.Wahed, A., & Ali, M. M. (2001). The skew-logistic distribution. J. Statist. Res, 35(2), 71-80.
[8] Glänzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory (pp. 75-84). Springer, Dordrecht.
[9] Glanzel, W. (1990). Some consequences of a characterization theorem based on truncated moments. Statistics, 21(4), 613-618.
[10] Gupta, R.C., and Gupta, R.D. (2004). Generalized Skew Normal Model, Test, 13, 501-524.
[11] Hamedani, G. G., Korkmaz, M. Ç., & Yousof, H. M. (2021). The type I quasi lambert family: properties, characterizations and different estimation methods. Pakistan Journal of Statistics and Operation Research, 17 (3), 545-558. 
[12] Harandi, S. S., and Alamatsaz, M. H. (2013). Alpha–Skew–Laplace distribution. Statistics and Probability Letters, 83(3), 774-782.
[13] Hasanalipour, P., and Sharafi, M. (2012). A New Generalized Balakrishnan Skew Normal Distribution, Stat Papers, 53, 219-228.
[14] Hazarika, P. J., and Chakraborty, S. (2014). Alpha-Skew-Logistic Distribution. IOSR Journal of Mathematics, 10(4), 36-46.
[15] Hazarika P. J., Shah, S. and Chakraborty, S. (2020). Balakrishnan Alpha Skew Normal Distribution: Properties and Applications. Malaysian Journal of Science, 39 (2), 71-91.
[16] Henze, N. (1986). A Probabilistic Representation of the Skew Normal Distribution, Scand. J. Stat., 13, 271–275.
[17] Huang, W. J., and Chen, Y. H. (2007). Generalized skew-Cauchy distribution. Statistics and Probability Letters, 77(11), 1137-1147.
[18] Jamalizadeheh, A., Behbooddian, J., and J. Balakrrishnan, N (2008). A Two Parameter Generalized Skew Normal Distribution, Stat. Prob. Lett., 78, 1722-1726.
[19] Ma, Y., and Genton, M.G. (2004). Flexible Class of Skew Symmetric Distributions, Scand  J  Statist., 31, 459–468.
[20] Louzada, F., Ara, A. and Fernandes, G. (2017). The bivariate alpha-skew-normal distribution. Communications in Statistics-Theory and Methods, 46(14), 7147-7156.
[21] Nekoukhou, V., and Alamatsaz, M.H., (2012), A family of skew-symmetric-Laplace distributions. Statistical Papers, 53(3), 685-696.
[22] Omar E., and Jawaher A. (2021) An accurate approximation for the standard normal distribution function, Journal of Information and Optimization Sciences, 42 (1), 17-27.
[23] Shafiei, S., Doostparast, M., and Jamalizadeh, A. (2016). The alpha–beta skew normal distribution: Properties and applications. Statistics, 50(2), 338-349.
[24] Shah, S., Chakraborty, S., and Hazarika, P. J.  (2020a). The Balakrishnan Alpha Skew Logistic Distribution: Properties and Applications. International Journal of Applied Mathematics and Statistics, 59(1), 76-92.
[25] Shah, S., Hazarika, P. J., and Chakraborty, S. (2020b). A New Alpha Skew Laplace Distribution: Properties and Its Applications. International Journal of Agricultural and Statistical Sciences, 16(1), 1-10.
[26] Shah, S., Hazarika, P. J., and Chakraborty, S. (2020c). The Balakrishnan Alpha Skew Truncated Cauchy Distribution with Applications in Modelling Currency Exchange Rate. Sains Malaysiana, 49(10), 2565-2571.
[27] Shah, S., Hazarika, P. J., Chakraborty, S., and Ali, M. M. (2020d). The Log-Balakrishnan-Alpha-Skew-Normal Distribution and Its Applications. Pakistan Journal of Statistics and Operation Research, 16(1), 109-117.
[28] Shah, S., Hazarika, P. J., Chakraborty, S., and Ali, M. M. (2021). A Generalized-Alpha-Beta-Skew Normal Distribution with Applications. Annals of Data Science, https://doi.org/10.1007/s40745-021-00325-0.
[29] Sharafi, M., and Behboodian, J. (2008). The Balakrishnan skew–normal density. Statistical Papers, 49(4), 769-778.
[30] 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.
[31] Venegas, O., Bolfarine, H., Gallardo, D. I., Vergara-Fernández, A., and Gómez, H. W. (2016). A Note on the Log Alpha Skew Normal Model with Geochemical Applications. Appl. Math, 10(5), 1697-1703.
[32] Wahed, A., and Ali, M. M. (2001). The skew-logistic distribution. J. Statist. Res, 35(2), 71-80.
[33] Yadegari, I., Gerami, A., and Khaledi, M.J. (2008). A generalization of the Balakrishnan skew normal distribution. Stat. Probab. Lett. 78: 1165-1167.

Views: 175Downloads: 8Citations: 1