On Characterizing the Exponential q-Distribution

  • Boutouria Imen
  • Bouzida ImedEmail author
  • Masmoudi Afif


In this paper, we attempted to characterize the exponential q-distribution through the q-memorylessness property using the q-addition operator and Jackson integral. Moreover, an extended version of k-gamma q-distribution is introduced and the q-moments of this family is computed. Finally, we suggested a new q-inversion method to simulate data from a q-distribution.


q-Calculus q-Gamma function k-Gamma q-distribution Exponential q-distribution 

Mathematics Subject Classification

44A20 33E20 33E50 


  1. 1.
    Ahmed, F., Kamel, B., Néji, B.: Asymptotic approximations in quantum calculus. J. Nonlinear Math. Phys. 12, 586–606 (2004)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Borges, E.P.: A possible deformed algebra and calculus inspired in nonextensive thermostatistics. J. Phys. A 340, 95–101 (2004)MathSciNetGoogle Scholar
  3. 3.
    Charalambos, A.C.: Discrete q-distributions on Bernoulli trials with a geometrically varying success probability. J. Stat. Plan. Inference 140, 2355–2383 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Charalambos, A.C.: Discrete q-distributions. Wiley, Hoboken (2016)CrossRefGoogle Scholar
  5. 5.
    Cheung, P., Kac, V.: Quantum Calculus. Springer, Berlin (2002)zbMATHGoogle Scholar
  6. 6.
    Chung, K.-S., Chung, W.-S., Nam, S.-T., Kang, H.-J.: New q-derivative and q-logarithm. Int. J. Theor. Phys. 33, 2019–2029 (1994)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Damak, M., Vladimir, G.: Self-adjoint operators affiliated to \( C^{*}\)-algebras. Rev. Math. Phys. 16, 257–280 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    De Sole, A., Kac, V.: On integral representations of q-gamma and q-beta functions. Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Lince Mat. Appl. 16, 11–29 (2005)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Díaz, R., Pariguan, E.: On the Gaussian q-distribution. J. Math. Anal. Appl. 358, 1–9 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Díaz, R., Ortiz, C., Pariguan, E.: On the k-gamma q-distribution. J. Math. Cent. Eur. 8(3), 448–458 (2010)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gaspard, B.: An introduction to q-difference equations (2007)Google Scholar
  12. 12.
    Ghany, H.A.: Levy–Khinchin type formula for basic completely monotone functions. Int. J. Pure Appl. Math. 87, 689–697 (2013)Google Scholar
  13. 13.
    Jackson, F.H.: On a q-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910)zbMATHGoogle Scholar
  14. 14.
    Jackson, F.H.: On a q-functions and a certain difference operator. Trans. R. Soc. Edinb. 46, 253–281 (1908)CrossRefGoogle Scholar
  15. 15.
    Mathai, A.M.: A pathway to matrix-variate gamma and normal densities. Linear Algebra Appl. 396, 317–328 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Srivastava, H.M., Choi, J.: Zeta and q-Zeta Functions and Associated Series and Integrals. Elsevier Science Publishers, Amsterdam (2012)zbMATHGoogle Scholar
  17. 17.
    Thomas, E.: A method for q-calculus. J. Nonlinear Math. Phys. 10, 487–525 (2003)MathSciNetCrossRefGoogle Scholar

Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Laboratory of Probability and StatisticsSfax UniversitySfaxTunisia

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