On the Ratio of Inverted Gamma Variates
DOI:
https://doi.org/10.17713/ajs.v36i2.328Abstract
In this paper the distribution and moments of the ratio of independent inverted gamma variates have been considered. Unbiased estimators of the parameter involved in the distribution have been proposed. As a particular case, the ratio of independent Levy variates have been studied.References
Abramowitz, M., and Stegtun, I. A. (1970). Handbook of Mathematical Functions. New York: Dover Publication Inc.
Ali, M. M., Woo, J., and Pal, M. (2006). Distribution of the ratio of generalized uniform variates. Pakistan Journal of Statistics, 22, 11-19.
Basu, A. P., and Lochner, R. H. (1979). On the distribution of the generalized life distributions. Technometrics, 33, 281-287.
Bowman, K. O., Shenton, L. R., and Gailey, P. C. (1998). Distribution of the ratio of gamma variates. Communications in Statistics – Simulation and Computation, 27, 1-19.
Gradshteyn, I. S., and Ryhzik, I. M. (1965). Tables of Integrals, Series and Products. New York: Academic Press.
Jurlewicz, A., and Weron, K. A. (1993). Relationship between asymmetric Levy-stable distributions and the dielectric susceptibility. Journal of Statistical Physics, 73, 69-81.
Korhonen, P. J., and Narula, S. C. (1989). The probability distribution of the ratio of the absolute values of two normal variables. Journal of Statistical Computation and Simulation, 33, 173-182.
Marsaglia, G. (1965). Ratios of normal variables and ratios of sums of uniform variables. Journal of the American Statistical Association, 60, 193-204.
Pham-Gia, T. (2000). Distributions of the ratios of independent beta variables and applications. Communications in Statistics – Theory and Methods, 29, 2693-2715.
Press, S. J. (1969). The t ratio distribution. Journal of the American Statistical Association, 64, 242-252.
Provost, S. B. (1989). On the distribution of the ratio of powers of sums of gamma random variables. Pakistan Journal of Statistics, 5, 157-174.
Downloads
Published
How to Cite
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
