Brazilian Journal of Probability and Statistics

Bivariate sinh-normal distribution and a related model

Debasis Kundu

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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.

Article information

Braz. J. Probab. Stat., Volume 29, Number 3 (2015), 590-607.

Received: July 2013
Accepted: December 2013
First available in Project Euclid: 11 June 2015

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Zentralblatt MATH identifier

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


Kundu, Debasis. Bivariate sinh-normal distribution and a related model. Braz. J. Probab. Stat. 29 (2015), no. 3, 590--607. doi:10.1214/13-BJPS235.

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