Product of independent random variables involving inverted hypergeometric function type I variables
Keywords:
appell's first hypergeometric function, beta distribution, Gauss hypergeometric function, Humbert’s confluent hypergeometric function, product, transformationAbstract
The inverted hypergeometric function type I distribution has the probability density function proportional to [formula] where 2F1 is the Gauss hypergeometric function. In this article, we derive the probability density function of the product of two independent random variables having inverted hypergeometric function type I distribution. We also consider several other products involving inverted hypergeometric function type I, beta type I, beta type II, beta type III, Kummer-beta and hypergeometric function type I variables.
MSC: 33Cxx
Downloads
References
A. K. Gupta and D. K. Nagar.Matrix variate distributions, ISBN 1–58488–046–5. Chapman & Hall/CRC. Boca Raton, 2000.
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).
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).
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).
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).
Michael B. Gordy. Computationally convenient distributional assumptions for common-value auctions. Computational Economics, ISSN 0927–7099, eISSN 1572–9974, 12(1), 61–78 (1998).
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.
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).
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).
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
H. M. Srivastava and P. W. Karlsson. Multiple Gaussian hypergeometric series, ISBN 0–470–20100–2. Halsted Press [John Wiley & Sons], New York, 1985.
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.
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.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Plagiarism Detection