Research Article Open Access

New Families of Distributions for Modeling Bivariate Data, with Applications

Haroon Barakat1, Osama Mohareb Khaled2 and Nourhan Khalil3
  • 1 Zagazig University, Egypt
  • 2 Port said University, Egypt
  • 3 Port Said University, Egypt

Abstract

In this study we introduce a new method of adding two shape parameters to any baseline bivariate distribution function (df) to get a more flexible family of bivariate df's. Through the additional parameters we can fully control the type of the resulting family. This method is applied to yield a new two-parameter extension of the bivariate standard normal distribution, denoted by BSSN. The statistical properties of the BSSN family are studied. Moreover, via a mixture of the BSSN family and the standard bivariate logistic df, we get a more capable family, denoted by FBSSN. Theoretically, each of the marginals of the FBSSN contains all the possible types of df's with respect to the signs of skewness and excess kurtosis. In addition, each possesses very wide range of the indices of skewness and kurtosis. Finally, we compare the families BSSN and FBSSN with some important competitors (i.e., some generalized families of bivariate df's) via real data examples. AMS 2010 Subject Classification: 62-07; 62E10; 62F99.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 79-87

DOI: https://doi.org/10.3844/jmssp.2018.79.87

Submitted On: 17 February 2018 Published On: 3 April 2018

How to Cite: Barakat, H., Khaled, O. M. & Khalil, N. (2018). New Families of Distributions for Modeling Bivariate Data, with Applications. Journal of Mathematics and Statistics, 14(1), 79-87. https://doi.org/10.3844/jmssp.2018.79.87

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Keywords

  • Bivariate Non-Normal Distribution
  • Parametric Family
  • Mixture Distributions
  • Bivariate Data Modeling