A Class of Power Series <i>q</i>-Distributions
A class of power series <i>q</i>-distributions, generated by considering a <i>q</i>-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its <i>q</i>-factorial moments are obtained in terms of <i>q</i>-derivatives of it...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/712 |
| _version_ | 1797264192393183232 |
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| author | Charalambos A. Charalambides |
| author_facet | Charalambos A. Charalambides |
| author_sort | Charalambos A. Charalambides |
| collection | DOAJ |
| description | A class of power series <i>q</i>-distributions, generated by considering a <i>q</i>-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its <i>q</i>-factorial moments are obtained in terms of <i>q</i>-derivatives of its series (parametric) function. Also, it is shown that the convolution of power series <i>q</i>-distributions is also a power series <i>q</i>-distribution. Furthermore, the <i>q</i>-Poisson (Heine and Euler), <i>q</i>-binomial of the first kind, negative <i>q</i>-binomial of the second kind, and <i>q</i>-logarithmic distributions are shown to be members of this class of distributions and their <i>q</i>-factorial moments are deduced. In addition, the convolution properties of these distributions are examined. |
| first_indexed | 2024-04-25T00:25:00Z |
| format | Article |
| id | doaj.art-f56aff02f0ed43a983452196230f01f0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-25T00:25:00Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f56aff02f0ed43a983452196230f01f02024-03-12T16:50:02ZengMDPI AGMathematics2227-73902024-02-0112571210.3390/math12050712A Class of Power Series <i>q</i>-DistributionsCharalambos A. Charalambides0Department of Mathematics, University of Athens, Panepistemiopolis, GR-15784 Athens, GreeceA class of power series <i>q</i>-distributions, generated by considering a <i>q</i>-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its <i>q</i>-factorial moments are obtained in terms of <i>q</i>-derivatives of its series (parametric) function. Also, it is shown that the convolution of power series <i>q</i>-distributions is also a power series <i>q</i>-distribution. Furthermore, the <i>q</i>-Poisson (Heine and Euler), <i>q</i>-binomial of the first kind, negative <i>q</i>-binomial of the second kind, and <i>q</i>-logarithmic distributions are shown to be members of this class of distributions and their <i>q</i>-factorial moments are deduced. In addition, the convolution properties of these distributions are examined.https://www.mdpi.com/2227-7390/12/5/712Euler distributionHeine distributionnegative <i>q</i>-binomial distribution<i>q</i>-binomial distribution<i>q</i>-factorial moments<i>q</i>-logarithmic distribution |
| spellingShingle | Charalambos A. Charalambides A Class of Power Series <i>q</i>-Distributions Mathematics Euler distribution Heine distribution negative <i>q</i>-binomial distribution <i>q</i>-binomial distribution <i>q</i>-factorial moments <i>q</i>-logarithmic distribution |
| title | A Class of Power Series <i>q</i>-Distributions |
| title_full | A Class of Power Series <i>q</i>-Distributions |
| title_fullStr | A Class of Power Series <i>q</i>-Distributions |
| title_full_unstemmed | A Class of Power Series <i>q</i>-Distributions |
| title_short | A Class of Power Series <i>q</i>-Distributions |
| title_sort | class of power series i q i distributions |
| topic | Euler distribution Heine distribution negative <i>q</i>-binomial distribution <i>q</i>-binomial distribution <i>q</i>-factorial moments <i>q</i>-logarithmic distribution |
| url | https://www.mdpi.com/2227-7390/12/5/712 |
| work_keys_str_mv | AT charalambosacharalambides aclassofpowerseriesiqidistributions AT charalambosacharalambides classofpowerseriesiqidistributions |