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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Main Authors: Christophe Chesneau, Veena D'cruz, R. Maya, M.R. Irshad
Format: Article
Language:English
Published: Instituto Nacional de Estatística | Statistics Portugal 2025-08-01
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
description 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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publishDate 2025-08-01
publisher Instituto Nacional de Estatística | Statistics Portugal
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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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