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On the q-Gamma distribution: Properties and inference

  • Nahla Ben Salah EMAIL logo , Afif Masmoudi and Khalil Masmoudi
Published/Copyright: December 12, 2025
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 75 Issue 6

Abstract

In this paper, we introduce a new q-Gamma probability distribution which is an extension of the classical Gamma distribution in the context of q-calculus. It is also a generalization of the q-exponential distribution. The main properties of the proposed model are presented. Its non-centered moments of any order were explicitly computed. In particular, the kurtosis and skewness were explicitly determined. Moreover, the maximum-likelihood estimation method of the parameters was developped. The performance of the estimation approach as well as the Metropolis-Hastings-based generation method were studied through several numerical experiments. In addition, a characterization of the q-exponential distribution is established using the truncated moments.

Keywords: q-Gamma distribution; q-exponential distribution; maximum likelihood estimation; moments; truncated moments
2020 Mathematics Subject Classification: Primary 60E05; 62E10; 62F10

We would like to thank Ministry of Higher Education and Scientific Research Tunisia for their continuous encouragement by project of young researcher 21 PEJC D1P03.

  1. (Communicated by Gejza Wimmer)

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Received: 2024-12-15
Accepted: 2025-08-16
Published Online: 2025-12-12
Published in Print: 2025-12-17

© 2025 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2025-0111
Keywords for this article
q-Gamma distribution; q-exponential distribution; maximum likelihood estimation; moments; truncated moments

Articles in the same Issue

  1. A new categorical equivalence for stone algebras
  2. On special classes of prime filters in BL-algebras
  3. A note on characterized and statistically characterized subgroups of 𝕋 = ℝ/ℤ
  4. New Young-type integral inequalities using composition schemes
  5. The structure of pseudo-n-uninorms with continuous underlying functions
  6. Jensen-type inequalities for a second-order differential inequality condition
  7. A direct proof of the characterization of the convexity of the discrete Choquet integral
  8. Envelope of plurifinely plurisubharmonic functions and complex Monge-Ampère type equation
  9. Fekete-Szegö inequalities for Φ-parametric and β-spirllike mappings of complex order in ℂn
  10. Entire function sharing two values partially with its derivative and a conjecture of Li and Yang
  11. Oscillatory properties of third-order semi-canonical dynamic equations on time scales via canonical transformation
  12. Weighted B-summability and positive linear operators
  13. Some properties and applications of convolution algebras
  14. On measures of σ-noncompactess in F-spaces
  15. On the kolmogorov–feller–gut weak law of large numbers for triangular arrays of rowwise and pairwise negatively dependent random variables
  16. Intermediately trimmed sums of oppenheim expansions: A strong law
  17. Novel weighted distribution: Properties, applications and web-tool
  18. On the q-Gamma distribution: Properties and inference
  19. Finiteorthoatomistic effect algebras and regular algebraic E-test spaces
  20. Prof. RNDr. Anatolij Dvurečenskij, DrSc. 75th anniversary
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