Research and Innovation Articles
Published 2010-09-21
Keywords
- Kummer-beta distribution,
- confluent hypergeometric function,
- Gauss hypergeometric function,
- moments
How to Cite
Sepúlveda Murillo, F. H. (2010). Exact and approximate distributions of the products of Kummer-beta variables. Revista Integración, Temas De matemáticas, 28(2), 101–109. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2170
Abstract
We present the exact distribution for the product Y = X1X2, where X1 and X2 are random variables with combined Kummer-beta distribution. We propose an approximate distribution exhibiting the performance of its adjustment.
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References
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[11] Witkovsky V., “Computing the distribution of a linear combination of inverted gamma variables”, Kybernetika, 37 (2001), 79–90.
[2] Garg M., Katta V., Gupta M.K., “Thde distribution of the products of powers of generalized Dirochlet components”, Kyungpook Math. J., 42 (2002), 429–436.
[3] Johnson N. L., Kotz S., and Balakrishnan N., Continuous Univariate Distributions, Vol. 2, Second Edition, John Wiley & Sons, New York, 1995.
[4] Nagar D. K., and Zarrazola E., “Distributions of the product and the quotient of independent Kummer-beta variables”, Scientiae Mathematicae Japonicae, 61 (2005), 109–117.
[5] Ng K. W., and Kotz S., Kummer-gamma and Kummer-beta univariate and multivariate distributions, Research Report, no. 84, Department of Statistics, The University of Hong Kong, Hong Kong, 1995.
[6] Pham-Gia T., and Turkkan N., “The product and quotient of general beta distributions”, Statistical Paper, 43 (2002), 537–550.
[7] Podolski H., “The distribution of a product of n independent random variables with generalized gamma distribution”, Demonstration Mathematica, 4 (1972), 119–123.
[8] Rathie P. N., and Rohrer H. G., “The exact distribution of products of independent random variables”, Metron, 45 (1987), 235–245.
[9] Sakamoto H., “On the distributions of the product and quotient of the independent and uniformly distributed random variables”, Tohoku Mathematical Journal, 49 (1943), 243–260.
[10] Sornette D., “Multiplicative processes and power laws”, Physical Review E, 57 (1998), 4811– 4813.
[11] Witkovsky V., “Computing the distribution of a linear combination of inverted gamma variables”, Kybernetika, 37 (2001), 79–90.