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

Received: 29 August 2019/Accepted: 17 March 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

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*Corresponding author; email: parthajhazarika@gmail.com