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
Transmuted Bivariate Distribution Dependence Bivariate Distribution Spearman’s Rho correlation coefficient Fréchet Bounds
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- [8] Bismi G., Bivariate Burr Distributions, unpublished PhD Thesis, Cochin University of Science and Technology, 2005.
- [9] Basu A.P., Bivariate Failure Rate, Journal of the American Statistical Association, 66 (1971) 103–104.
- [10] Johnson N. L. and Kotz S., A Vector Multivariate Hazard Rate, Journal of Multivariate Analysis, 5-1 (1975) 53-66.
- [11] Roy D., A Characterization of Model Approach for Generating Bivariate Life Distributions Using Reversed Hazard Rates, Journal of Japan Statistical Society, 32-2 (2002) 239–245.
- [12] Hoeffding W., Masstabinvariante Korrelationstheorie, Schriften des Mathematischen Instituts und Instituts fur Angewandte Mathematik der Universitat Berlin, 5 (1940) 181-233.
- [13] Fréchet M., Sur Les Tableaux de Corrélation Dont Les marges Sont Donnees, Annales de l’Université de Lyon, Sciences, 4 (1951) 13–84.
- [14] Schweizer B. and Wolff E., On Nonparametric Measures of Dependence for Random Variables, The Annals of Statistics, 9-4 (1981) 879-885.
- [15] Yela P.J. and Cuevas T.J.R., Estimating the Gumbel-Barnett Copula Parameter of Dependence, Revista Colombiana de Estadística, 41-1 (2018) 53-73.
Abstract
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.
- [9] Basu A.P., Bivariate Failure Rate, Journal of the American Statistical Association, 66 (1971) 103–104.
- [10] Johnson N. L. and Kotz S., A Vector Multivariate Hazard Rate, Journal of Multivariate Analysis, 5-1 (1975) 53-66.
- [11] Roy D., A Characterization of Model Approach for Generating Bivariate Life Distributions Using Reversed Hazard Rates, Journal of Japan Statistical Society, 32-2 (2002) 239–245.
- [12] Hoeffding W., Masstabinvariante Korrelationstheorie, Schriften des Mathematischen Instituts und Instituts fur Angewandte Mathematik der Universitat Berlin, 5 (1940) 181-233.
- [13] Fréchet M., Sur Les Tableaux de Corrélation Dont Les marges Sont Donnees, Annales de l’Université de Lyon, Sciences, 4 (1951) 13–84.
- [14] Schweizer B. and Wolff E., On Nonparametric Measures of Dependence for Random Variables, The Annals of Statistics, 9-4 (1981) 879-885.
- [15] Yela P.J. and Cuevas T.J.R., Estimating the Gumbel-Barnett Copula Parameter of Dependence, Revista Colombiana de Estadística, 41-1 (2018) 53-73.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 31, 2019 |
| Submission Date | September 10, 2019 |
| Acceptance Date | October 2, 2019 |
| Published in Issue | Year 2019Volume: 40 Issue: 4 |