Producto de variables aleatorias independentes que involucran variables con función hipergeométrica invertida de tipo I
Main Article Content
Keywords
primera función hipergeométrica de Appell, distribución beta, función hipergeométrica confluente de Humbert, función hipergeométrica de Gauss, producto, transformación
Resumen
La distribución de función hipergeométrica invertida tipo I tiene la función de densidad de probabilidad proporcional a [fórmula] donde 2F1 es la función hipergeométrica de Gauss. En este artículo se deriva la función de densidad de probabilidad del producto de dos variables aleatorias independientes que se distribuyen según la función hipergeométrica inversa tipo I. También se consideran otros productos entre variables aleatorias con distribución beta tipo I, beta tipo II, beta tipo III, función hipergeométrica tipo I, función hipergeométrica inversa tipo I y Kummer–beta.
MSC: 33Cxx
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Referencias
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[13] A. M. Mathai. A handbook of generalized special functions for statistical and physical sciences, ISBN 0–198–53595–3.Oxford University Press, New York, 1993.
[2] Daya K. Nagar and José A. Álvarez. Properties of the hypergeometric function type I distribution. Advances and Applications in Statistics, ISSN 0972–3617, 5(3), 341–351 (2005).
[3] A. M. Mathai and R. K. Saxena. Distribution of product and the structural set up of densities. Annals of Mathematical Statistics, ISSN 0003–4851, 40(4), 1439— 1448 (1969).
[4] D. K. Nagar and E. Zarrazola. Distributions of the product and the quotient of independent Kummer–beta variables. Scientiae Mathematicae Japonicae, ISSN 1346–0862, eISSN 1346–0447, 61(1), 109–117 (2005).
[5] Luz E. S´anchez and Daya K. Nagar. Distributions of the product and quotient of independent beta type 3 variables. Far East Journal of Theoretical Statistics, ISSN 0972–0863, 17(2), 239–251 (2005).
[6] Michael B. Gordy. Computationally convenient distributional assumptions for common-value auctions. Computational Economics, ISSN 0927–7099, eISSN 1572–9974, 12(1), 61–78 (1998).
[7] N. L. Johnson, S. Kotz and N. Balakrishnan, Continuous Univariate Distributions-2, second edition, ISBN 978-0-471-58494-0. John Wiley & Sons, New York, 1994.
[8] A. K. Gupta and D. K. Nagar. Matrix variate beta distribution. International Journal of Mathematics and Mathematical Sciences, ISSN 0161–1712, eISSN 1687–0425, 24(7), 449–459 (2000).
[9] D. K. Nagar and A. K. Gupta. Matrix variate Kummer–beta distribution. Jour- nal of the Australian Mathematical Society, ISSN 1446–7887, eISSN 1446–8107, 73(1), 11–25 (2002).
[10] Y. L. Luke. The special functions and their approximations, vol. 1, ISBN 0– 124–59901–X. Academic Press, New York, 1969. Referenced in 104, 105
[11] H. M. Srivastava and P. W. Karlsson. Multiple Gaussian hypergeometric series, ISBN 0–470–20100–2. Halsted Press [John Wiley & Sons], New York, 1985.
[12] A. M. Mathai and R. K. Saxena. The H-function with applications in statistics and other disciplines, ISBN 0–852–26559–X. Halsted Press [John Wiley & Sons], New York, 1978.
[13] A. M. Mathai. A handbook of generalized special functions for statistical and physical sciences, ISBN 0–198–53595–3.Oxford University Press, New York, 1993.