A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency

Hüseyin Ünözkan; Mehmet Yılmaz

doi:10.17776/csj.742159

EN

A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency

Abstract

In this study, a new approach to transmutation theory is developed by using negative dependency basement. Once choosing a distribution that has negative dependency with the same marginal, a new bivariate distribution is derived. In this study, we examined a new transmutation technique in which a negative dependency offers a big success in modeling rather than most known and used statistical distributions. This approach clash with classical transmutation methods. In this study at the beginning, the classical transmutation is defined. Later, we introduce the new technique and obtain lower and upper bounds of distribution to show that this approach gives us a distribution. Gaining new bivariate continuous distributions with this technique may be more appropriate in theory, and modeling of some data sets in terms of this approach may be more efficient.

Keywords

Transmuted bivariate distribution, Dependence, Bivariate distribution, Negative dependency, Fréchet bounds

References

[1] Dolati A., Ubeda-Flores M., Constructing Copulas by Means of Pairs of Order Statistics, Kybernetika, 45(6) (2009) 992-1002.
[2] Lai C. D., Xie M., A New Family of Positive Quadrant Dependent Bivariate Distributions, Statistics and Probability Letters, 46(4) (2000) 359-364.
[3] Kimeldorf G., Sampson A.R., A Framework for Positive Dependence, Ann. Inst. Statist. Math., 41(1) (1989) 31-45.
[4] 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.
[5] Shaw W.T., Buckley I.R.C., The Alchemy of Probability Distributions:Beyond Gram-Charlier & Cornish-Fisher Expansions,and Skew-Normal or Kurtotic-Normal Distributions, Financial Mathematics Group, King’s College, 1 (28) (2007).
[6] Aryal G.R., Tsokos C.P., On the transmuted extreme value distribution with application. Nonlinear Analysis, Theory, Methods & Applications, 71 (12) (2009) 1401-1407.
[7] Aryal G.R., Tsokos C.P., Transmuted Weibull Distribution, European Journal of Pure and Applied Mathematics, 4 (2) (2011) 89-102.
[8] Merovci F., Transmuted Lindley Distribution, Int. J. Open Problems Compt. Math., 6 (2) (2013) 63-72.
[9] Merovci F., Transmuted Exponentiated Exponential Distribution, Mathematical Sciences and Applications E-Notes, 1 (2) (2013) 112-122.
[10] Merovci F., Transmuted Rayleigh Distribution, Austrian Journal of Statistics, 42 (1) (2013) 21-31.

[11] Aryal G.R., Transmuted Log-Logistic Distribution, Journal of Statistics Applications & Probability, 2 (1) (2013) 11-20.
[12] Elbatal I., Diab L.S. and AbdulAlim N.A., Transmuted Generalized Linear Exponential Distribution, International Journal of Computer Applications, 83 (17) 82013) 29-37.
[13] Merovci F., Puka L., Transmuted Pareto distribution, ProbStat Forum, 7 (2014) 1-11.
[14] Mohamed H.A., Transmuted Exponentiated Gamma Distribution: A Generalization of the Exponentiated Gamma Probability Distribution, Applied Mathematical Sciences, 8 (27) (2014) 1297-1310.
[15] Oguntunde E.P., Adejumo O.A., The Transmuted Inverse Exponential Distribution, International Journal of Advanced Statistics and Probability, 3 (1) 82015) 1-7.
[16] Ünözkan H., Yılmaz M., A New Method for Generating Distributions: An Application to Flow Data, International Journal of Statistics and Applications, 9 (3) (2019) 92-99
[17] Barlow R. E., Proschan, F., Statistical Theory of Reliability and Life Testing: Probability Models, Technical Report, New York: Holt, Rinehart and Winston, 1975.
[18] 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.
[19] Farlie D., The Performance of Some Correlation Coefficients for a General Bivariate Distribution, Biometrika, 47(3/4) (1960) 307-323.
[20] Gumbel E. J., Bivariate Exponential Distributions, Journal of the American Statistical Association, 55-292 (1960) 698-707.
[21] Bismi G., Bivariate Burr Distributions, unpublished PhD Thesis, Cochin University of Science and Technology, 2005.
[22] Basu A.P., Bivariate Failure Rate, Journal of the American Statistical Association, 66 (1971) 103–104.
[23] Hoeffding W., Masstabinvariante Korrelationstheorie, Schriften des Mathematischen Instituts und Instituts fur Angewandte Mathematik der Universitat Berlin, 5 (1940) 181-233.
[24] Fréchet M., Sur Les Tableaux de Corrélation Dont Les marges Sont Donnees, Annales de l’Université de Lyon, Sciences, 4 (1951) 13–84.
[25] Schweizer B. and Wolff E., On Nonparametric Measures of Dependence for Random Variables, The Annals of Statistics, 9(4) (1981) 879-885.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

Hüseyin Ünözkan ^*
0000-0001-9659-287X
Türkiye

Mehmet Yılmaz
0000-0002-9762-6688
Türkiye

Publication Date

December 29, 2020

Submission Date

May 24, 2020

Acceptance Date

August 19, 2020

Published in Issue

Year 2020 Volume: 41 Number: 4

DOI

https://doi.org/10.17776/csj.742159

IZ

https://izlik.org/JA77SN42BM

APA

Ünözkan, H., & Yılmaz, M. (2020). A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency. Cumhuriyet Science Journal, 41(4), 938-943. https://doi.org/10.17776/csj.742159

AMA

1.Ünözkan H, Yılmaz M. A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency. CSJ. 2020;41(4):938-943. doi:10.17776/csj.742159

Chicago

Ünözkan, Hüseyin, and Mehmet Yılmaz. 2020. “A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency”. Cumhuriyet Science Journal 41 (4): 938-43. https://doi.org/10.17776/csj.742159.

EndNote

Ünözkan H, Yılmaz M (December 1, 2020) A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency. Cumhuriyet Science Journal 41 4 938–943.

IEEE

[1]H. Ünözkan and M. Yılmaz, “A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency”, CSJ, vol. 41, no. 4, pp. 938–943, Dec. 2020, doi: 10.17776/csj.742159.

ISNAD

Ünözkan, Hüseyin - Yılmaz, Mehmet. “A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency”. Cumhuriyet Science Journal 41/4 (December 1, 2020): 938-943. https://doi.org/10.17776/csj.742159.

JAMA

1.Ünözkan H, Yılmaz M. A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency. CSJ. 2020;41:938–943.

MLA

Ünözkan, Hüseyin, and Mehmet Yılmaz. “A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency”. Cumhuriyet Science Journal, vol. 41, no. 4, Dec. 2020, pp. 938-43, doi:10.17776/csj.742159.

Vancouver

1.Hüseyin Ünözkan, Mehmet Yılmaz. A New Approach to Bivariate Transmutation: Construction of Continuous Bivariate Distribution Under Negative Dependency. CSJ. 2020 Dec. 1;41(4):938-43. doi:10.17776/csj.742159

Cited By

The assessment of insurance risk premium with a simulation study using Archimedean copulas

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

https://doi.org/10.31801/cfsuasmas.1583979

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December