An Extended Lagrangian Zero-Truncated Poisson Distribution: Theory and Applications

Amira F. Daghestani; Hassan S. Bakouch; Radhakumari Maya; Muraleedharan Pushpa Sarath Lal; C. Subramanian; Anhar S. Aloufi; Muhammed Rasheed Irshad

doi:10.3390/sym18081335

An Extended Lagrangian Zero-Truncated Poisson Distribution: Theory and Applications

Amira F. Daghestani
, Hassan S. Bakouch^*
, Radhakumari Maya
, Muraleedharan Pushpa Sarath Lal
, C. Subramanian
, Anhar S. Aloufi
, Muhammed Rasheed Irshad

^*Corresponding author for this work

Qassim University
Cochin University of Science and Technology
Annamalai University
University of Jeddah

Research output: Contribution to journal › Article › peer-review

Abstract

An extended Lagrangian zero-truncated Poisson (ELZTP) distribution is proposed as a new member of the Lagrangian distributions of the second kind. The model provides a flexible framework for capturing diverse dispersion patterns and tail behaviors. Key statistical properties are derived, including the probability mass function, moments, entropy, and the hazard rate function. Parameters are estimated using the maximum likelihood method, and the finite-sample behavior of the estimators is investigated through a simulation study. The effectiveness of the model is demonstrated using a real-life air-pollution dataset, highlighting the adaptability of the ELZTP distribution to environmental count data applications.

Original language	English
Article number	1335
Pages (from-to)	1-23
Number of pages	23
Journal	Symmetry
Volume	18
Issue number	8
DOIs	https://doi.org/10.3390/sym18081335
State	Published - Aug 2026

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 4 Quality Education
SDG 9 Industry, Innovation, and Infrastructure

Keywords

data modeling
entropy
Lagrangian distributions
maximum likelihood estimation
overdispersion
simulation
underdispersion

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10.3390/sym18081335

Cite this

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title = "An Extended Lagrangian Zero-Truncated Poisson Distribution: Theory and Applications",

abstract = "An extended Lagrangian zero-truncated Poisson (ELZTP) distribution is proposed as a new member of the Lagrangian distributions of the second kind. The model provides a flexible framework for capturing diverse dispersion patterns and tail behaviors. Key statistical properties are derived, including the probability mass function, moments, entropy, and the hazard rate function. Parameters are estimated using the maximum likelihood method, and the finite-sample behavior of the estimators is investigated through a simulation study. The effectiveness of the model is demonstrated using a real-life air-pollution dataset, highlighting the adaptability of the ELZTP distribution to environmental count data applications.",

keywords = "data modeling, entropy, Lagrangian distributions, maximum likelihood estimation, overdispersion, simulation, underdispersion",

author = "Daghestani, \{Amira F.\} and Bakouch, \{Hassan S.\} and Radhakumari Maya and Lal, \{Muraleedharan Pushpa Sarath\} and C. Subramanian and Aloufi, \{Anhar S.\} and Irshad, \{Muhammed Rasheed\}",

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year = "2026",

month = aug,

doi = "10.3390/sym18081335",

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AU - Daghestani, Amira F.

AU - Bakouch, Hassan S.

AU - Maya, Radhakumari

AU - Lal, Muraleedharan Pushpa Sarath

AU - Subramanian, C.

AU - Aloufi, Anhar S.

AU - Irshad, Muhammed Rasheed

PY - 2026/8

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N2 - An extended Lagrangian zero-truncated Poisson (ELZTP) distribution is proposed as a new member of the Lagrangian distributions of the second kind. The model provides a flexible framework for capturing diverse dispersion patterns and tail behaviors. Key statistical properties are derived, including the probability mass function, moments, entropy, and the hazard rate function. Parameters are estimated using the maximum likelihood method, and the finite-sample behavior of the estimators is investigated through a simulation study. The effectiveness of the model is demonstrated using a real-life air-pollution dataset, highlighting the adaptability of the ELZTP distribution to environmental count data applications.

AB - An extended Lagrangian zero-truncated Poisson (ELZTP) distribution is proposed as a new member of the Lagrangian distributions of the second kind. The model provides a flexible framework for capturing diverse dispersion patterns and tail behaviors. Key statistical properties are derived, including the probability mass function, moments, entropy, and the hazard rate function. Parameters are estimated using the maximum likelihood method, and the finite-sample behavior of the estimators is investigated through a simulation study. The effectiveness of the model is demonstrated using a real-life air-pollution dataset, highlighting the adaptability of the ELZTP distribution to environmental count data applications.

KW - data modeling

KW - entropy

KW - Lagrangian distributions

KW - maximum likelihood estimation

KW - overdispersion

KW - simulation

KW - underdispersion

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DO - 10.3390/sym18081335

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EP - 23

JO - Symmetry

JF - Symmetry

IS - 8

M1 - 1335

ER -

An Extended Lagrangian Zero-Truncated Poisson Distribution: Theory and Applications

Abstract

UN SDGs

Keywords

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