Sains Malaysiana 49(10)(2020): 2565-2571

http://dx.doi.org/10.17576/jsm-2020-4910-22

The Balakrishnan Alpha Skew Truncated Cauchy Distribution with Applications in Modelling Currency Exchange Rate

(Pencongan Alfa Balakrishnan Taburan Cauchy Terpenggal dengan Aplikasi dalam Pemodelan Pertukaran Kadar Matawang)

SRICHARAN SHAH, PARTHA JYOTI HAZARIKA* & SUBRATA CHAKRABORTY

Department of Statistics, Dibrugarh University, Dibrugarh, Assam, 786004, India

Diserahkan: 29 Ogos 2019/Diterima: 17 Mac 2020

ABSTRACT

In this article, a new class of alpha skew truncated Cauchy distribution is proposed by considering Balakrishnan methodology and investigated some of its related distributions. This article also derive various properties of this distribution along with its moments. The proposed distribution is applied in modeling currency exchange rate data with some other existing distributions, viz., skewed Cauchy distribution, skewed truncated Cauchy distribution, truncated skew Cauchy uniform distribution, doubly truncated skew Cauchy distribution, and alpha skew truncated Cauchy distribution. Based on the model selection criteria, Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC), the proposed distribution has shown significant improvement in modeling exchange rate dataset.

Keywords: Alpha-skew distribution; alpha-skew-truncated-Cauchy distribution; Balakrishnan alpha-skew-normal distribution; bimodal distribution; skew distribution

ABSTRAK

Dalam makalah ini, kelas baharu taburan Cauchy terpenggal pencong alfa dicadangkan dengan mempertimbangkan kaedah Balakrishnan dan beberapa taburan yang berkaitan dikaji. Makalah ini juga menerbitkan pelbagai sifat taburan bersama dengan momennya. Taburan yang dicadangkan digunakan dalam pemodelan data kadar pertukaran mata wang bersama dengan beberapa taburan sedia ada, iaitu, taburan Cauchy terpencong, taburan Cauchy terpenggal pencong, taburan seragam Cauchy terpenggal pencong, taburan Cauchy terpenggal pencong dua kali, dan taburan Cauchy terpenggal pencong alfa. Berdasarkan kriteria pemilihan model, Kriteria Maklumat Akaike (AIC) dan Kriteria Maklumat Bayesian (BIC), taburan yang dicadangkan mempunyai peningkatan yang signifikan dalam pemodelan set data kadar pertukaran.

Kata kunci: Taburan bimodal; taburan Cauchy terpenggal pencong alfa; taburan normal pencong alfa Balakrishnan; taburan pencong alfa; taburan pencong

RUJUKAN

Alhamide, A.A., Ibrahim, K., Alodat, M.T. & Zin, W.Z.W. 2019. Bayesian inference for linear regression under alpha-skew-normal prior. Sains Malaysiana 48(1): 227-235.

Arnold, B.C. & Beaver, R.J. 2000. The Skew-Cauchy distribution. Statistics & Probability Letters 49(3): 285-290.

Ashani, Z.N., Bakar, M.R.A., Ibrahim, N.A. & Adam, M.B. 2016. A skewed truncated Cauchy uniform distribution and its moment. Modern Applied Science 10(7): 174-182.

Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12(2):171-178.

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.

Chakraborty, S. & Hazarika, P.J. 2011. A survey of the theoretical developments in univariate skew normal distributions. Assam Statistical Review 25(1): 41-63.

Elal-Olivero, D. 2010. Alpha-skew-normal distribution. Proyecciones (Antofagasta) 29(3): 224-240.

Hazarika, P.J. & Chakraborty, S. 2016. Application of alpha skew truncated Cauchy distribution in exchange rate data. Journal of Statistical Distributions and Applications 2(2): 22-26.

Hazarika, P.J. & Chakraborty, S. 2014. Alpha-skew-logistic distribution. IOSR Journal of Mathematics 10(4): 36-46.

Hazarika, P.J., Shah, S. & Chakraborty, S. 2019. Balakrishnan alpha skew normal distribution: Properties and applications. Malaysian Journal of Science 39(2): 71-91.

Huang, W.J. & Chen, Y.H. 2007. Generalized Skew-Cauchy distribution. Statistics & Probability Letters 77(11): 1137-1147.

Nadarajah, S. & Kotz, S. 2007. A skewed truncated Cauchy distribution with applications in economics. Applied Economics Letters 14(13): 957-961.

Prudnikov, A.P., Brychkov, I.A. & Marichev, O.I. 1986. Integrals and Series: Special Functions.  Amsterdam: Gordon and Breach Science Publishers.

Shah, S., Chakraborty, S. & Hazarika, P.J. 2020a. A new one parameter bimodal skew logistic distribution and its applications. arXiv Preprint arXiv:1906.04125.

Shah, S., Hazarika, P.J. & Chakraborty, S. 2020b. The Balakrishnan alpha skew Laplace distribution: Properties and its applications. arXiv Preprint arXiv:1910.01084.

*Pengarang untuk surat-menyurat; email: parthajhazarika@gmail.com