Open Access

ARTICLE

The Arcsine-X Family of Distributions with Applications to Financial Sciences

by Yen Liang Tung¹, Zubair Ahmad², Eisa Mahmoudi^2,*

1 Accounting Department, School of Business, Nanjing University, Nanjing 210093, China
2 Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran

* Corresponding Author: Eisa Mahmoudi. Email:

Computer Systems Science and Engineering 2021, 39(3), 351-363. https://doi.org/10.32604/csse.2021.014270

Received 01 September 2020; Accepted 09 October 2020; Issue published 12 August 2021

Abstract

The heavy-tailed distributions are very useful and play a major role in actuary and financial management problems. Actuaries are often searching for such distributions to provide the best fit to financial and economic data sets. In the current study, a prominent method to generate new distributions useful for modeling heavy-tailed data is considered. The proposed family is introduced using trigonometric function and can be named as the Arcsine-X family of distributions. For the purposes of the demonstration, a specific sub-model of the proposed family, called the Arcsine-Weibull distribution is considered. The maximum likelihood estimation method is adopted for estimating the parameters of the Arcsine-X distributions. The resultant estimators are evaluated in a detailed Monte Carlo simulation study. To illustrate the Arcsine-Weibull two insurance data sets are analyzed. Comparison of the Arcsine-Weibull model is done with the well-known two parameters and four parameters competitors. The competitive models including the Weibull, Lomax, Burr-XII and beta Weibull models. Different goodness of fit measures are taken into account to determine the usefulness of the Arcsine-Weibull and other considered models. Data analysis shows that the Arcsine-Weibull distribution works much better than competing models in financial data analysis.

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Citations