본문 바로가기
KERD
논문KCI 등재

On characterizing the gamma and the beta $q$-distributions

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, our central focus is upon gamma and beta $q$-distributions from a probabilistic viewpoint. The gamma and the beta $q$-distributions are characterized by investing the nature of the joint $q$-probability density function through the $q$-independence property and the $q$-Laplace transform.

Abstract

In this paper, our central focus is upon gamma and beta $q$-distributions from a probabilistic viewpoint. The gamma and the beta $q$-distributions are characterized by investing the nature of the joint $q$-probability density function through the $q$-independence property and the $q$-Laplace transform.

참고문헌 (24)

  1. W. H. Abdi, "On q-Laplace transforms", Proc. Nat. Acad. Sci. India Sect. A, 29, pp.389~408 (1960)
  2. W. H. Abdi, "On certain q-difference equations and q-Laplace transform", Proc. Nat. Inst. Sci. India Part A, 28, pp.1~15 (1962)
  3. W. H. Abdi, "Application of q-Laplace transform to the solution of certain q-integral equations", Rend. Circ. Mat. Palermo (2), 11, pp.245~257 (1962)[DOI]
  4. W. H. Abdi, "Certain inversion and representation formulae for q-Laplace transforms", Math. Z., 83, pp.238~249 (1964)[DOI]
  5. A. N. Ahmed, "Characterization of beta, binomial, and Poisson distributions", IEEE Transactions on Reliability, 40(3), pp.290~295 (1991)[DOI]
  6. M. H. Al-Ashwal, "Leibniz's Rule and Fubini's Theorem Associated with Power Quantum Difference Operators", International Journal of Mathematical Analysis, 9(55), pp.2733~2747 (2015)[DOI]
  7. G. Bangerezako, "An introduction to q-difference equations" (2007)
  8. M. Bohner, "The h-Laplace and q-Laplace transforms", J. Math. Anal. Appl., 365(1), pp.75~92 (2010)[DOI]
  9. Ch. A. Charalambides, "Discrete q-distributions on Bernoulli trials with a geometrically varying success probability", J. Statist. Plann. Inference, 140(9), pp.2355~2383 (2010)[DOI]
  10. K.-S. Chung, "New q-derivative and q-logarithm", Internat. J. Theoret. Phys., 33(10), pp.2019~2029 (1994)[DOI]
  11. A. De Sole, "On integral representations of q-gamma and q-beta functions", Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 16(1), pp.11~29 (2005)
  12. R. Diaz, "On the k-gamma q-distribution", Cent. Eur. J. Math., 8(3), pp.448~458 (2010)[DOI]
  13. R. Diaz, "On the Gaussian q-distribution", J. Math. Anal. Appl., 358(1), pp.1~9 (2009)[DOI]
  14. T. Ernst, "A method for q-calculus", J. Nonlinear Math. Phys., 10(4), pp.487~525 (2003)[DOI]
  15. P. Findeisen, "A simple proof of a classical theorem which characterizes the gamma distribution", Ann. Statist., 6(5), pp.1165~1167 (1978)[DOI]
  16. A. Fitouhi, "Asymptotic approximation in quantum calculus", J. Nonlinear Math. Phys., 12(4), pp.586~606 (2005)[DOI]
  17. H. Gauchman, "Integral inequalities in q-calculus", Comput. Math. Appl., 47(2-3), pp.281~300 (2004)[DOI]
  18. T.-Y. Hwang, "On a characterization of the gamma distribution: the independence of the sample mean and the sample coefficient of variation", Ann. Inst. Statist. Math., 51(4), pp.749~753 (1999)[DOI]
  19. V. Kac, "Quantum Calculus, Universitext" (2002), Springer-Verlag
  20. B. Kolodziejek, "Characterization of beta distribution on symmetric cones", J. Multivariate Anal., 143, pp.414~423 (2016)[DOI]
  21. I. Kotlarski, "On characterizing the gamma and the normal distribution", Pacific J. Math., 20, pp.69~76 (1967)[DOI]
  22. E. Lukacs, "A characterization of the gamma distribution", Ann. Math. Statist., 26, pp.319~324 (1955)[DOI]
  23. A. M. Mathai, "A pathway to matrix-variate gamma and normal densities", Linear Algebra Appl., 396, pp.317~328 (2005)[DOI]
  24. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier, Inc.

관련 논문AI추천

이 간행물의 다른 논문 (21건)