Some Results on the Free Poisson Distribution Article Swipe
Ayed R. A. Alanzi
,
Ohud A. Alqasem
,
Maysaa Elmahi Abd Elwahab
,
Raouf Fakhfakh
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3390/axioms13080496
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.3390/axioms13080496
Let K+(μi)={Qsiμi,si∈(m0μi,m+μi)}, i=1,2, be two CSK families generated by the nondegenerate probability measures μ1 and μ2 with support bounded from above. Define the set of measures L=K+(μ1)•K+(μ2)={Qs1μ1•Qs2μ2,s1∈(m0μ1,m+μ1)ands2∈(m0μ2,m+μ2)}, where Qs1μ1•Qs2μ2 denotes the Fermi convolution of Qs1μ1 and Qs2μ2. We prove that if L is still a CSK family (that is, L=K+(σ) for some nondegenerate probability measure ()σ), then the probability measures σ, μ1 and μ2 are of the free Poisson type and follow the free Poisson law up to affinity. The same result, regarding the free Poisson measure, is obtained if we consider the t-deformed free convolution t replacing the Fermi convolution • in the family of measures L.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/axioms13080496
- https://www.mdpi.com/2075-1680/13/8/496/pdf?version=1721824811
- OA Status
- gold
- Cited By
- 1
- References
- 18
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4400944072
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https://doi.org/10.3390/axioms13080496Digital Object Identifier
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Some Results on the Free Poisson DistributionWork title
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articleOpenAlex work type
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enPrimary language
- Publication year
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2024Year of publication
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2024-07-24Full publication date if available
- Authors
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Ayed R. A. Alanzi, Ohud A. Alqasem, Maysaa Elmahi Abd Elwahab, Raouf FakhfakhList of authors in order
- Landing page
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https://doi.org/10.3390/axioms13080496Publisher landing page
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2075-1680/13/8/496/pdf?version=1721824811Direct OA link when available
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Poisson distribution, Convolution (computer science), Mathematics, Probability measure, Measure (data warehouse), Bounded function, Combinatorics, Mathematical analysis, Statistics, Computer science, Database, Machine learning, Artificial neural networkTop concepts (fields/topics) attached by OpenAlex
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| referenced_works | https://openalex.org/W6637516499, https://openalex.org/W4292235929, https://openalex.org/W1600303801, https://openalex.org/W2964011754, https://openalex.org/W2314742568, https://openalex.org/W1925318460, https://openalex.org/W1570229043, https://openalex.org/W1594682445, https://openalex.org/W4233185824, https://openalex.org/W2963009812, https://openalex.org/W1988344476, https://openalex.org/W2964180569, https://openalex.org/W6858178048, https://openalex.org/W2318335932, https://openalex.org/W3098442735, https://openalex.org/W3102394916, https://openalex.org/W4388130149, https://openalex.org/W4294656594 |
| referenced_works_count | 18 |
| abstract_inverted_index.L | 41 |
| abstract_inverted_index.a | 44 |
| abstract_inverted_index.t | 96 |
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| abstract_inverted_index.CSK | 5, 45 |
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| abstract_inverted_index.μ2 | 15, 63 |
| abstract_inverted_index.σ, | 60 |
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| abstract_inverted_index.i=1,2, | 2 |
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| abstract_inverted_index.Qs2μ2. | 36 |
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| abstract_inverted_index.convolution | 32, 95, 100 |
| abstract_inverted_index.probability | 11, 53, 58 |
| abstract_inverted_index.nondegenerate | 10, 52 |
| abstract_inverted_index.Qs1μ1•Qs2μ2 | 28 |
| abstract_inverted_index.K+(μi)={Qsiμi,si∈(m0μi,m+μi)}, | 1 |
| abstract_inverted_index.L=K+(μ1)•K+(μ2)={Qs1μ1•Qs2μ2,s1∈(m0μ1,m+μ1)ands2∈(m0μ2,m+μ2)}, | 26 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 90 |
| corresponding_author_ids | https://openalex.org/A5089048863 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 4 |
| corresponding_institution_ids | https://openalex.org/I142899784, https://openalex.org/I199702508 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.5899999737739563 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile.value | 0.75683446 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |