ON THE DISTRIBUTION OF THE PRODUCTS AND QUOTIENT OF INVERSE BURR DISTRIBUTED RANDOM VARIABLES BASED ON FGM COPULA
Keywords:
Inverse Burr distribution, Gauss Hypergeometric function, products, quotient of random variablesAbstract
In this article, Inverse Burr Distribution based on Farlie-Gumbel-Morgenstern copula is introduced. Derivations of exact distribution V = XY, W = X/Y, and Z = X/(X+Y) are obtained in closed form. Corresponding moment properties of these distributions are also derived. The expressions turn out to involve known special functions.
References
Balakrishnan, N., & Lai, C.D. (2009). Continuous Bivariate Distributions. New York: Springer.
Coelho, C.A., & Mexia, J.T. (2007). On the Distribution of the Product and Ratio of Independent Generalized Gamma-Ratio Random Variables. Sankhy?: The Indian Journal of Statistics, 221-255.
Mcneil, A., Frey, R., & Embrechts, P. (2005). Quantitative Risk Management. Princeton University Press, New Jersey.
Morgenstern, D. (1956). Einfache Beispiele Zweidimensionaler Verteilungen. Mitteilingsblatt fur Mathematische Statistik. 8, 234-235.
Nadarajah, S. (2005). Sums, Products, and Ratios for the Bivariate Gumbel Distribution. Mathematical and Computer Modelling, 42 (5), 499-518.
Nadarajah, S., & Espejo, M. R. (2006). Sums, Products, and Ratios for the Generalized Bivariate Pareto Distribution. Kodai Mathematical Journal, 29 (1), 72-83.
Nadarajah, S., & Kotz, S. (2007). On the Convolution of Pareto and Gamma Distributions. Computer Networks, 51 (12), 3650-3654.
Nelsen, R.B. (2003, September). Properties and Applications of Copulas: A brief survey. In Proceedings of the First Brazilian Conference on Statistical Modeling in Insurance and Finance, (Dhaene, J., Kolen, N., Morettin, PA (Eds.), University Press USP: Sao Paulo (pp.10-28).
Patton, A. (2012). Copula Methods for Forecasting Multivarate Times Series. In Handbook of Economic Forecasting, Volume 2. Springer Verlog.
Rohatgi, V. K., Saleh, A. M. E. (2015). An introduction to Probability and Statistics. John Wiley & Sons.
Salvadori, G., Michele C. D., Kottegoda, N., & Rosso, R. (2007). Extremes in Nature: An Approach Using Copulas. Water Science and Technology Library, Vol. 56. Springer.
Schmidt, T. (2007). Coping with Copulas. Copulas-From Theory to Application in Finance, 3-34.
Sklar, M. (1959). Fonctions de r´e Partition `a n Dimensions et Leurs Marges. Universit´e Paris 8.
Trivedi, P. K., & Zimmer, D. M. (2007). Copula Modeling: An Introduction for Practitioners. Now Publishers Inc.
Coelho, C.A., & Mexia, J.T. (2007). On the Distribution of the Product and Ratio of Independent Generalized Gamma-Ratio Random Variables. Sankhy?: The Indian Journal of Statistics, 221-255.
Mcneil, A., Frey, R., & Embrechts, P. (2005). Quantitative Risk Management. Princeton University Press, New Jersey.
Morgenstern, D. (1956). Einfache Beispiele Zweidimensionaler Verteilungen. Mitteilingsblatt fur Mathematische Statistik. 8, 234-235.
Nadarajah, S. (2005). Sums, Products, and Ratios for the Bivariate Gumbel Distribution. Mathematical and Computer Modelling, 42 (5), 499-518.
Nadarajah, S., & Espejo, M. R. (2006). Sums, Products, and Ratios for the Generalized Bivariate Pareto Distribution. Kodai Mathematical Journal, 29 (1), 72-83.
Nadarajah, S., & Kotz, S. (2007). On the Convolution of Pareto and Gamma Distributions. Computer Networks, 51 (12), 3650-3654.
Nelsen, R.B. (2003, September). Properties and Applications of Copulas: A brief survey. In Proceedings of the First Brazilian Conference on Statistical Modeling in Insurance and Finance, (Dhaene, J., Kolen, N., Morettin, PA (Eds.), University Press USP: Sao Paulo (pp.10-28).
Patton, A. (2012). Copula Methods for Forecasting Multivarate Times Series. In Handbook of Economic Forecasting, Volume 2. Springer Verlog.
Rohatgi, V. K., Saleh, A. M. E. (2015). An introduction to Probability and Statistics. John Wiley & Sons.
Salvadori, G., Michele C. D., Kottegoda, N., & Rosso, R. (2007). Extremes in Nature: An Approach Using Copulas. Water Science and Technology Library, Vol. 56. Springer.
Schmidt, T. (2007). Coping with Copulas. Copulas-From Theory to Application in Finance, 3-34.
Sklar, M. (1959). Fonctions de r´e Partition `a n Dimensions et Leurs Marges. Universit´e Paris 8.
Trivedi, P. K., & Zimmer, D. M. (2007). Copula Modeling: An Introduction for Practitioners. Now Publishers Inc.
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2019-01-02
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