Construction of Continuous Bivariate Distribution by Transmuting Dependent Distribution
Abstract
In this study, a new bivariate distribution family is introduced by adding an appropriate term to independent class. By choosing a base distribution which is negatively dependent from the same marginals we derive a new distribution around the product of marginals, i.e. independent class of distribution. We note that the new distribution has additional parameter which would provide additional flexibility in applications. The joint probability density, joint reliability and reversed hazard rate functions of the new bivariate distribution are obtained. Furthermore, we obtain lower and upper bounds of Spearman’s correlation coefficient. Two example are given to illustrate this family. This new bivariate continuous distribution can make more appropriate modeling of some data sets in terms of the Spearman rank coefficient.
Keywords
References
- [1] Dolati A. and Ubeda-Flores M., Constructing Copulas by Means of Pairs of Order Statistics, Kybernetika, 45-6 (2009) 992-1002.
- [2] Lai C. D. and Xie M., A New Family of Positive Quadrant Dependent Bivariate Distributions, Statistics and Probability Letters, 46-4 (2000) 359-364.
- [3] Han Kwang-Hee., A New Family of Negative Quadrant Dependent Bivariate Distributions with Continuous Marginal, Journal of the Chungcheong Mathematical Society, 24-4 (2011) 795-805.
- [4] Technical Report, Holt, Rinehart and Winston, New York, 1975.
- [5] Domma F., Bivariate Reversed Hazard Rate, Notions, and Measures of Dependence and their Relationships, Communications in Statistics - Theory and Methods, 40-6 (2011) 989-999, DOI: 10.1080/03610920903511777.
- [6] Farlie D., The Performance of Some Correlation Coefficients for a General Bivariate Distribution, Biometrika, 47-3/4 (1960) 307-323.
- [7] Gumbel E. J., Bivariate Exponential Distributions, Journal of the American Statistical Association, 55-292 (1960) 698-707.
- [8] Bismi G., Bivariate Burr Distributions, unpublished PhD Thesis, Cochin University of Science and Technology, 2005.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
December 31, 2019
Submission Date
September 10, 2019
Acceptance Date
October 2, 2019
Published in Issue
Year 2019 Volume: 40 Number: 4
Cited By
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