A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables
The distribution of the sum of two independent Lindley random variables having the same parameter defines the 2S-Lindley distribution recently introduced in the statistical literature. In this paper, we use it to create a new one-parameter discrete compound distribution called the Poisson 2S-Lindle...
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Instituto Nacional de Estatística | Statistics Portugal
2025-08-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/599 |
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| author | Christophe Chesneau Veena D'cruz R. Maya M.R. Irshad |
| author_facet | Christophe Chesneau Veena D'cruz R. Maya M.R. Irshad |
| author_sort | Christophe Chesneau |
| collection | DOAJ |
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The distribution of the sum of two independent Lindley random variables having the same parameter defines the 2S-Lindley distribution recently introduced in the statistical literature. In this paper, we use it to create a new one-parameter discrete compound distribution called the Poisson 2S-Lindley distribution. The mathematical and statistical properties of the proposed distribution are investigated and analyzed systematically. Subsequently, a statistical standpoint is adopted. Various estimation methods are considered, and an extensive simulation study is conducted to compare them. A count regression model as well as a first-order integer-valued autoregressive process based on the proposed model are constructed. In total, four real data sets in different fields are used to prove the empirical importance of the distribution.
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| format | Article |
| id | doaj-art-a74a9785f301422196a3a4a64779d2e8 |
| institution | DOAJ |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-a74a9785f301422196a3a4a64779d2e82025-08-20T03:02:07ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-08-01233A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random VariablesChristophe Chesneau 0https://orcid.org/0000-0002-1522-9292Veena D'cruz1https://orcid.org/0000-0002-3261-5902R. Maya2https://orcid.org/0000-0003-1138-740XM.R. Irshad3https://orcid.org/0000-0002-5999-1588Université de Caen Basse-NormandieCochin University of Science and TechnologyGovernment College for WomenCochin University of Science and Technology The distribution of the sum of two independent Lindley random variables having the same parameter defines the 2S-Lindley distribution recently introduced in the statistical literature. In this paper, we use it to create a new one-parameter discrete compound distribution called the Poisson 2S-Lindley distribution. The mathematical and statistical properties of the proposed distribution are investigated and analyzed systematically. Subsequently, a statistical standpoint is adopted. Various estimation methods are considered, and an extensive simulation study is conducted to compare them. A count regression model as well as a first-order integer-valued autoregressive process based on the proposed model are constructed. In total, four real data sets in different fields are used to prove the empirical importance of the distribution. https://revstat.ine.pt/index.php/REVSTAT/article/view/5992S-Lindley distributioncompoundingmomentsstress strength reliabilitysimulationcount regression model |
| spellingShingle | Christophe Chesneau Veena D'cruz R. Maya M.R. Irshad A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables Revstat Statistical Journal 2S-Lindley distribution compounding moments stress strength reliability simulation count regression model |
| title | A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables |
| title_full | A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables |
| title_fullStr | A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables |
| title_full_unstemmed | A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables |
| title_short | A Novel Discrete Distribution Based on the Mixture of Poisson and Sum of Two Lindley Random Variables |
| title_sort | novel discrete distribution based on the mixture of poisson and sum of two lindley random variables |
| topic | 2S-Lindley distribution compounding moments stress strength reliability simulation count regression model |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/599 |
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