Balakrishnan Alpha Skew Generalized t Distribution: Properties and Applications

Dimpal Pathak; Sricharan Shah; Partha Jyoti Hazarika; Subrata Chakraborty; Jondeep Das

doi:10.17485/IJST/v16iSP2.7587

Article

Balakrishnan Alpha Skew Generalized t Distribution: Properties and Applications

VIEWS 301
PDF 67

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16iSP2.7587

Year: 2023, Volume: 16, Issue: Special Issue 2, Pages: 44-52

Original Article

Balakrishnan Alpha Skew Generalized t Distribution: Properties and Applications

Dimpal Pathak^1*, Sricharan Shah², Partha Jyoti Hazarika³, Subrata Chakraborty⁴, Jondeep Das¹

¹Research Scholar, Department of Statistics, Dibrugarh University, Dibrugarh, 786002, Assam, India
²Department of Statistics, Dibrugarh University, Dibrugarh, Assam, India
³Assistant Professor, Department of Statistics, Dibrugarh University, Dibrugarh, Assam, India
⁴Professor, Department of Statistics, Dibrugarh University, Dibrugarh, Assam, India

*Corresponding Author
Email: [email protected]

Received Date:23 March 2023, Accepted Date:26 June 2023, Published Date:02 November 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: In this study, a new class of Balakrishnan distribution by extending the alpha skew generalized t distribution is proposed. Methods: Statistical properties of the Balakrishnan alpha skew generalized t distribution are studied in detail. In particular, specific expressions of the density and distribution function, moments, skewness, kurtosis and mode of the particular distribution are derived. The parameters of the new family of distributions are estimated by the method of maximum likelihood. Lastly, the flexibility, suitability and usefulness of the proposed distribution are illustrated by analyzing real-life data set. Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are used for model selection. Findings: The proposed distribution performs well in terms of AIC and BIC in real-life data modelling than the other symmetric and asymmetric distributions considered here. Novelty: The main uniqueness of the proposed distribution is to modal bimodal and heavy/light-tailed datasets.

Keywords: Skewed Distribution, Alpha Skew Generalized t Distribution, AIC, BIC, Optimization, Generalized t

References

Mcdonald JB, Newey WK. Partially Adaptive Estimation of Regression Models via the Generalized T Distribution. Econometric Theory. 2010;4(3):428–457. Available from: https://doi.org/10.1017/S0266466600013384
Azzalini A. A Class of Distributions Which Includes the Normal Ones. Scandinavian Journal of Statistics. 1985;12(2):171–178. Available from: http://www.jstor.org/stable/4615982
Duarte J, Martínez-Flórez G, Gallardo DI, Venegas O, Gómez HW. A Bimodal Extension of the Epsilon-Skew-Normal Model. Mathematics. 2023;11(3):1–18. Available from: https://doi.org/10.3390/math11030507
Shah S, Hazarika PJ, Pathak D, Chakraborty S, Ali MM. The Multimodal Extension of the Balakrishnan Alpha Skew Normal Distribution: Properties and Applications. Pakistan Journal of Statistics and Operation Research. 2023;19(1):203–217. Available from: https://doi.org/10.18187/pjsor.v19i1.4019
Shah S, Hazarika PJ, Chakraborty S, Alizadeh M. The Balakrishnan-Alpha-Beta-Skew-Laplace Distribution: Properties and Applications. Statistics, Optimization & Information Computing. 2023;11(3):755–772. Available from: https://doi.org/10.19139/soic-2310-5070-1247
Arslan O. The skew generalized t (SGT) distribution: properties and its applications in robust estimation. Book of Abstracts. 2011;p. 6. Available from: https://www.researchgate.net/publication/255647126_The_skew_generalized_t_SGT_distribution_properties_and_its_applications
Hazarika PJ, Shah S, Chakraborty S. Balakrishnan Alpha Skew Normal Distribution: Properties and Applications. 2019. Available from: https://doi.org/10.48550/arXiv.1906.07424
Acitas S, Senoglu B, Arslan O. Alpha-skew generalized t distribution. Revista Colombiana de Estadística. 2015;38(2):353–370. Available from: https://www.redalyc.org/pdf/899/89940050004.pdf
Arnold BC, Beaver RJ, Azzalini A, Balakrishnan N, Bhaumik A, Dey DK, et al. Skewed multivariate models related to hidden truncation and/or selective reporting. Test. 2002;11:7–54. Available from: https://doi.org/10.1007/BF02595728
Arnold BC, Beaver RJ, Azzalini A, Balakrishnan N, Bhaumik A, Dey DK, et al. Skewed multivariate models related to hidden truncation and/or selective reporting. Test. 2002;11:7–54. Available from: https://link.springer.com/article/10.1007/BF02595728
Shah S, Hazarika PJ, Chakraborty S. The Balakrishnan alpha skew Laplace distribution: Properties and its applications. 2019. Available from: https://doi.org/10.48550/arXiv.1910.01084
Shah S, Hazarika PJ. The Alpha-Beta-Skew-Logistic Distribution And Its Applications. 2019. Available from: https://doi.org/10.48550/arXiv.1910.01084
Elal-Olivero D. Alpha-skew-normal distribution. Proyecciones (Antofagasta, On line). 2011;29(3):224–240. Available from: http://dx.doi.org/10.4067/S0716-09172010000300006
Korkmaz MÇ, Toibourani EF, Kioye JY, Chesneau C. The Alpha-Skew Hyperbolic Secant Distribution with Applications to an Astronomical Dataset. Nicel Bilimler Dergisi. 2022;4(1):70–84. Available from: https://doi.org/10.51541/nicel.1021116
Kumar CS, Manju L. Gamma Generalized Logistic Distribution: Properties and Applications. Journal of Statistical Theory and Applications. 2022;21:155–174. Available from: https://doi.org/10.1007/s44199-022-00046-0
Adubisi OD, Abdulkadir A, Farouk UA, Chiroma H. The exponentiated half logistic skew-t distribution with GARCH-type volatility models. Scientific African. 2022;16:1–14. Available from: https://doi.org/10.1016/j.sciaf.2022.e01253
Guan R, Zhao X, Cheng W, Rong Y. A New Generalized t Distribution Based on a Distribution Construction Method. Mathematics. 2021;9(19):1–36. Available from: https://doi.org/10.3390/math9192413
Hazarika PJ, Shah S, Chakraborty S. The Balakrishnan Alpha-Skew-Normal Distribution: Properties and Applications. Malaysian Journal of Science. 2020;39(2):71–91. Available from: https://doi.org/10.22452/mjs.vol39no2.5
Shah S, Hazarika PJ, Chakraborty S. The alpha–beta skew normal distribution: properties and applications. 2019. Available from: https://doi.org/10.48550/arXiv.1910.01084
Nadarajah S. On the generalized t(GT) distribution. Statistics. 2008;42(5):467–473. Available from: https://doi.org/10.1080/02331880701747660
Gupta AK, Nadarajah S. Handbook of Beta Distribution and Its Applications (1). (pp. 1-600) Boca Raton, Florida, USA. CRC Press. 2004.
Hazarika PJ, Chakraborty S. Alpha-Skew-Logistic Distribution. IOSR Journal of Mathematics. 2014;10(4):36–46. Available from: https://doi.org/10.9790/5728-10463646
Harandi SS, Alamatsaz MH. Alpha-skew-Laplace distribution. Statistics & Probability Letters. 2013;83(3):774–782. Available from: https://doi.org/10.1016/j.spl.2012.11.024
Shafiei S, Doostparast M, Jamalizadeh A. The alpha–beta skew normal distribution: properties and applications. Statistics. 2016;50(2):338–349. Available from: https://doi.org/10.1080/02331888.2015.1096938
Esmaeili H, Lak F, Alizadeh M, Monfared MED. The Alpha-Beta Skew Logistic Distribution: Properties and Applications. Statistics, Optimization & Information Computing. 2020;8(1):304–317. Available from: https://doi.org/10.19139/soic-2310-5070-706
Lak F, Alizadeh M, Monfared MED, Esmaeili H. The Alpha-Beta Skew Generalized t Distribution: Properties and Applications. Pakistan Journal of Statistics and Operation Research. 2019;15(3):605–616. Available from: https://doi.org/10.18187/pjsor.v15i3.2404

Copyright

© 2023 Pathak et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)