Table of Contents Author Guidelines Submit a Manuscript
Journal of Probability and Statistics
Volume 2014, Article ID 982013, 6 pages
http://dx.doi.org/10.1155/2014/982013
Research Article

On -Gamma and -Beta Distributions and Moment Generating Functions

Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Received 10 February 2014; Revised 29 June 2014; Accepted 4 July 2014; Published 15 July 2014

Academic Editor: Chin-Shang Li

Copyright © 2014 Gauhar Rahman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. D. Rainville, Special Functions, The Macmillan, New York, NY, USA, 1960. View at MathSciNet
  2. R. Diaz, and E. Pariguan, “On hypergeometric functions and Pochhammer k-symbol,” Divulgaciones Matematicas, vol. 15, no. 2, pp. 179–192, 2007. View at Google Scholar · View at MathSciNet · View at Scopus
  3. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics, vol. 2, Charles Griffin and Company, London, UK, 1961.
  4. R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications, Prentice-Hall International, 5th edition, 2011.
  5. C. Walac, A Hand Book on Statictical Distributations for Experimentalist, 2007.
  6. C. G. Kokologiannaki, “Properties and inequalities of generalized k-gamma, beta and zeta functions,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 13–16, pp. 653–660, 2010. View at Google Scholar · View at MathSciNet
  7. C. G. Kokologiannaki and V. Krasniqi, “Some properties of the k-gamma function,” Le Matematiche, vol. 68, no. 1, pp. 13–22, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. V. Krasniqi, “A limit for the {$k$}-gamma and {$k$}-beta function,” International Mathematical Forum, vol. 5, no. 33, pp. 1613–1617, 2010. View at Google Scholar · View at MathSciNet
  9. M. Mansoor, “Determining the k-generalized gamma function ΓK𝒳 by functional equations,” Journal of Contemporary Mathematical Sciences, vol. 4, no. 2, pp. 1037–1042, 2009. View at Google Scholar
  10. S. Mubeen and G. M. Habibullah, “An integral representation of some k-hypergeometric functions,” International Mathematical Forum, vol. 7, no. 1–4, pp. 203–207, 2012. View at Google Scholar · View at MathSciNet
  11. S. Mubeen and G. M. Habibullah, “k-fractional integrals and application,” International Journal of Contemporary Mathematical Sciences, vol. 7, no. 1–4, pp. 89–94, 2012. View at Google Scholar · View at MathSciNet
  12. S. Mubeen, M. Naz, and G. Rahman, “A note on k-hypergemetric differential equations,” Journal of Inequalities and Special Functions, vol. 4, no. 3, pp. 38–43, 2013. View at Google Scholar · View at MathSciNet
  13. S. Mubeen, G. Rahman, A. Rehman, and M. Naz, “Contiguous function relations for k-hypergeometric functions,” ISRN Mathematical Analysis, vol. 2014, Article ID 410801, 6 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. Mubeen, M. Naz, A. Rehman, and G. Rahman, “Solutions of k-hypergeometric differential equations,” Journal of Applied Mathematics, vol. 2014, Article ID 128787, 13 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  15. F. Merovci, “Power product inequalities for the Γk function,” International Journal of Mathematical Analysis, vol. 4, no. 21, pp. 1007–1012, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  16. S. Mubeen, A. Rehman, and F. Shaheen, “Properties of k-gamma, k-beta and k-psi functions,” Bothalia Journal, vol. 4, pp. 371–379, 2014. View at Google Scholar
  17. A. Rehman, S. Mubeen, N. Sadiq, and F. Shaheen, “Some inequalities involving k-gamma and k-beta functions with applications,” Journal of Inequalities and Applications, vol. 2014, article 224, 16 pages, 2014. View at Publisher · View at Google Scholar