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A NOTE ON MODIFIED DEGENERATE GAMMA RANDOM VARIABLES

김원주|TAEKYUN KIM|DAE SAN KIM|권종겸
장전수학회 (Jangjeon Mathematical Society)|2024.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제1호|pp. 91-95|DOI 10.17777/pjms.2024.27.1.008

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참고문헌

키워드

modified degenerate gamma functionmodified degenerate gamma random variable
주제분류수학

초록

Let X and Y be independent random variables which are respectively the modified gamma random variable with parameters α1 and β, and that with parameters α2 and β. The aim of this note is to find the joint probability density function of U = X +Y and V = X X+Y , which gives a partial solution to an open problem.

Abstract

Let X and Y be independent random variables which are respectively the modified gamma random variable with parameters α1 and β, and that with parameters α2 and β. The aim of this note is to find the joint probability density function of U = X +Y and V = X X+Y , which gives a partial solution to an open problem.

참고문헌 (17)

  1. Akel, M., "On degenerate gamma matrix functions and related functions", Linear Multilinear Algebra, 71(4), pp.673~691 (2023)
  2. Aydin, M. S., "A new construction on the degenerate Hurwitz-zeta function associated with certain applications", Proc. Jangjeon Math. Soc, 25(2), pp.195~203 (2022)
  3. Jang, L., "A note on derangement polynomials and degenerate derangement polynomials", Adv. Stud. Contemp. Math. (Kyungshang), 31(4), pp.457~470 (2021)
  4. Jang, L. -C., "Some identities involving derangement polynomials and numbers and moments of gamma random variables", J. Funct. Spaces (2020)
  5. Kim, D. S., "On λ-linear functionals arising from p-adic integrals on Zp", Adv. Difference Equ (2021)
  6. Kim, T., "A note on degenerate gamma function and degenerate Stirling number of the second kind", Adv. Stud. Contemp. Math. (Kyungshang), 28(2), pp.207~214 (2018)
  7. Kim, T., "Note on the degenerate gamma function", Russ. J. Math. Phys, 27(3), pp.352~358 (2020)
  8. Kim, T., "Degenerate Laplace transform and degenerate gamma function", Russ. J. Math. Phys, 24(2), pp.241~248 (2017)
  9. Kim, T., "Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function", Adv. Difference Equ (2021)
  10. Kim, T., "A series transformation formula and related degenerate polynomials", Adv. Stud. Contemp. Math. (Kyungshang), 32(2), pp.121~136 (2022)
  11. Kim, T., "Advanced Mathematical Analysis and its Applications", pp.2023, Chapman and Hall
  12. Kim, T., "Degenerate binomial coefficients and degenerate hypergeometric functions", Adv. Difference Equ (2020)
  13. Kim, Y., "A note on modified degenerate gamma and Laplace transformation", Symmetry, 10, pp.1~8 (2018)
  14. Nantomah, K., "Certain Properties of the Modified Degenerate Gamma Function", Journal of Mathematics (2021)
  15. Ross, S. M., "Introduction to probability models" (2019), Academic Press
  16. Rudin, W., "Principles of mathematical analysis" (1976), McGraw-Hill Publishing Company
  17. Upadhyaya, L. M., "On the degenerate Laplace transform-I", Bulletin of Pure and Applied Sciences, 37E(1), pp.1~8 (2018)

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