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Kavitha Devi, M.
- A New Generalisation of Sam-solai's Multivariate Cauchy Distribution of Type-I
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Authors
Affiliations
1 Associate Professor of Mathematics, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, IN
2 Assistant Professor, Jamal Institute of Management, Jamal Mohamed College, Tiruchirappalli, South India, IN
3 Assistant Professor in Mathematics, V.M.K.V. Engineering College, Salem, Tamilnadu, IN
1 Associate Professor of Mathematics, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, IN
2 Assistant Professor, Jamal Institute of Management, Jamal Mohamed College, Tiruchirappalli, South India, IN
3 Assistant Professor in Mathematics, V.M.K.V. Engineering College, Salem, Tamilnadu, IN
Source
Global Journal of Theoretical and Applied Mathematics Sciences, Vol 2, No 1 (2012), Pagination: 49-61Abstract
This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distributions. More specifically the author visualizes a new generalization of Multivariate Cauchy distribution of Type-I from the univariate Cauchy distribution. Further, the Marginal, Conditional and Bi-variate case of this distribution was also discussed. Moreover, it is found that the Mean, Variance, product moments and generating functions of Sam's Multivariate and Bi-variate conditional Cauchy distribution are also undefined due to nature and non-convergence of the probability integral.Keywords
Sam-solai’s Multivariate Cauchy Distribution, Standard Cauchy Distribution, Cumulative Cauchy DistributionReferences
- Arnold, B. C. and Beaver, R. J. (2000). The skew-Cauchy distribution. Statist. Probab. Lett. 49, 285-290.
- I.S. Gradshteyn and I.M. Ryzhik (2000), Table of Integrals, Series, and Products (sixth edition), Academic Press, San Diego, CA.
- A.P. Prudnikov, Y.A. Brychkov and O.I. Marichev (1986) , Integrals and Series (vol. 1, 2 and 3), Gordon and Breach Science Publishers, Amsterdam.
- Branco, M. D. and Dey, D. K. (2001). A general class of multivariate skewelliptical distributions. J. Multivariate Anal. 79, 99-113.
- Arnold, B. C. and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test 11, 7-54.
- Genton, M. G. and Loper_do, N. (2002). Generalized skew-elliptical distributions and their quadratic forms. Institute of Statistics Mimeo Series #2539, to appear in Ann. Inst.Statist. Math.
- S. Nadarajah and S. Kotz, (2006) A truncated Cauchy distribution, Internat. J. Math. Ed. Sci. Tech.37, 605 – 607.
- A New Generalisation of Sam-solai's Multivariate Cauchy Distribution of Type-II
Abstract Views :319 |
PDF Views:0
Authors
Affiliations
1 Associate Professor of Mathematics, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, IN
2 Assistant Professor, Jamal Institute of Management, Jamal Mohamed College, Tiruchirappalli, South India, IN
3 Assistant Professor in Mathematics, V.M.K.V. Engineering College, Salem, Tamilnadu, IN
1 Associate Professor of Mathematics, Jamal Mohamed College, Tiruchirappalli, Tamilnadu, IN
2 Assistant Professor, Jamal Institute of Management, Jamal Mohamed College, Tiruchirappalli, South India, IN
3 Assistant Professor in Mathematics, V.M.K.V. Engineering College, Salem, Tamilnadu, IN
Source
Global Journal of Theoretical and Applied Mathematics Sciences, Vol 2, No 1 (2012), Pagination: 63-75Abstract
This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distributions. More specifically the author visualizes a new generalization of Multivariate Cauchy distribution of Type-II from the univariate Cauchy distribution. Further, the Marginal, Conditional and Bi-variate case of this distribution was also discussed. Moreover, it is found that the Mean, Variance, product moments and generating functions of Sam-Solai's Multivariate and Bi-variate conditional Cauchy distribution are also undefined due to nature and non-convergence of the probability integral.References
- Arnold, B. C. and Beaver, R. J. (2000). The skew-Cauchy distribution. Statist. Probab. Lett. 49, 285-290.
- I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products (sixth edition), Academic Press, San Diego, CA., 2000
- A.P. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integrals and Series (vol. 1, 2 and 3), Gordon and Breach Science Publishers, Amsterdam, 1986
- Branco, M. D. and Dey, D. K. (2001). A general class of multivariate skewelliptical distributions. J. Multivariate Anal. 79, 99-113.
- Arnold, B. C. and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting. Test 11, 7-54.
- Genton, M. G. and Loper_do, N. (2002). Generalized skew-elliptical distributions and their quadratic forms. Institute of Statistics Mimeo Series #2539, to appear in Ann. Inst. Statist. Math.
- S. Nadarajah and S. Kotz, (2006) A truncated Cauchy distribution, Internat. J. Math. Ed. Sci. Tech.37,605–607.