Open Access
August 2015 Bivariate sinh-normal distribution and a related model
Debasis Kundu
Braz. J. Probab. Stat. 29(3): 590-607 (August 2015). DOI: 10.1214/13-BJPS235


Sinh-normal distribution is a symmetric distribution with three parameters. In this paper, we introduce bivariate sinh-normal distribution, which has seven parameters. Due to presence of seven parameters it is a very flexible distribution. Different properties of this new distribution has been established. The model can be obtained as a bivariate Gaussian copula also. Therefore, using the Gaussian copula property, several properties of this proposed distribution can be obtained. Maximum likelihood estimators cannot be obtained in closed forms. We propose to use two step estimators based on Copula, which can be obtained in a more convenient manner. One data analysis has been performed to see how the proposed model can be used in practice. Finally, we consider a bivariate model which can be obtained by transforming the sinh-normal distribution and it is a generalization of the bivariate Birnbaum–Saunders distribution. Several properties of the bivariate Birnbaum–Saunders distribution can be obtained as special cases of the proposed generalized bivariate Birnbaum–Saunders distribution.


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Debasis Kundu. "Bivariate sinh-normal distribution and a related model." Braz. J. Probab. Stat. 29 (3) 590 - 607, August 2015.


Received: 1 July 2013; Accepted: 1 December 2013; Published: August 2015
First available in Project Euclid: 11 June 2015

zbMATH: 1326.62028
MathSciNet: MR3355749
Digital Object Identifier: 10.1214/13-BJPS235

Keywords: Birnbaum–Saunders distribution , bivariate Birnbaum–Saunders distribution , copula , log-Birnbaum–Saunders distribution , maximum likelihood estimators , total positivity of order two , two stage estimators

Rights: Copyright © 2015 Brazilian Statistical Association

Vol.29 • No. 3 • August 2015
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