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A Class of Power Series q -Distributions

Author

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  • Charalambos A. Charalambides

    (Department of Mathematics, University of Athens, Panepistemiopolis, GR-15784 Athens, Greece)

Abstract

A class of power series q -distributions, generated by considering a q -Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q -factorial moments are obtained in terms of q -derivatives of its series (parametric) function. Also, it is shown that the convolution of power series q -distributions is also a power series q -distribution. Furthermore, the q -Poisson (Heine and Euler), q -binomial of the first kind, negative q -binomial of the second kind, and q -logarithmic distributions are shown to be members of this class of distributions and their q -factorial moments are deduced. In addition, the convolution properties of these distributions are examined.

Suggested Citation

  • Charalambos A. Charalambides, 2024. "A Class of Power Series q -Distributions," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:712-:d:1347903
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    References listed on IDEAS

    as
    1. Andreas George Kyriakoussis & Malvina Vamvakari, 2013. "A q-Analogue of the Stirling Formula and a Continuous Limiting Behaviour of the q-Binomial Distribution—Numerical Calculations," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 187-213, March.
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