A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic

Irshad, Muhammed Rasheed; Chesneau, Christophe; Shibu, Damodaran Santhamani; Monisha, Mohanan; Maya, Radhakumari

doi:10.3390/stats5040060

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…The values λ, μ, and ρ obtained by maximizing L n with respect to λ, µ, and ρ, respectively, are the ML estimates (MLEs). Upon differentiating the log-likelihood function given in (18) with respect to the parameters λ, µ, and ρ, respectively, and equating to zero, we obtain the following likelihood equations:…”

Section: Estimationmentioning

confidence: 99%

“…Our team was very impressed by the competency of the distributions proposed based on the Lagrangian method, and as a result, we proposed the Lagrangian version of ZTPD through the work published in [17]. Furthermore, the authors in [18] concentrated on the Lagrangian approach's construction of the zero-truncated binomial distribution (ZTBD) and explained how effective it was in comparison to other zero-truncated distributions. The aforementioned relevance once more compelled us to develop solutions to intervention problems using a Lagrangian approach, which we dub the LIPD.…”

Section: Introductionmentioning

confidence: 99%

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A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

Irshad

Monisha

Chesneau

et al. 2023

Stats

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The zero-truncated Poisson distribution (ZTPD) generates a statistical model that could be appropriate when observations begin once at least one event occurs. The intervened Poisson distribution (IPD) is a substitute for the ZTPD, in which some intervention processes may change the mean of the rare events. These two zero-truncated distributions exhibit underdispersion (i.e., their variance is less than their mean). In this research, we offer an alternative solution for dealing with intervention problems by proposing a generalization of the IPD by a Lagrangian approach called the Lagrangian intervened Poisson distribution (LIPD), which in fact generalizes both the ZTPD and the IPD. As a notable feature, it has the ability to analyze both overdispersed and underdispersed datasets. In addition, the LIPD has a closed-form expression of all of its statistical characteristics, as well as an increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rate function. A consequent part is devoted to its statistical application. The maximum likelihood estimation method is considered, and the effectiveness of the estimates is demonstrated through a simulated study. To evaluate the significance of the new parameter in the LIPD, a generalized likelihood ratio test is performed. Subsequently, we present a new count regression model that is suitable for both overdispersed and underdispersed datasets using the mean-parametrized form of the LIPD. Additionally, the LIPD’s relevance and application are shown using real-world datasets.

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Section: Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

Irshad

Monisha

Chesneau

et al. 2023

Stats

Self Cite

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“…Furthermore, the authors in [18] also used the LD 2 to create the generalized LKD of type two. The competence of the distributions proposed based on the LD 2 profoundly attracted our team, and as a result, we suggested the Lagrangian version of the ZTPD, the zero-truncated binomial distribution, and the IPD (see [26][27][28]). Moreover, the authors in [24] demonstrated that every member of the LD 2 was also a member of the LD 1 .…”

Section: Introductionmentioning

confidence: 99%

A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences

et al. 2023

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In this article, the Lagrange expansion of the second kind is used to generate a novel zero-truncated Katz distribution; we refer to it as the Lagrangian zero-truncated Katz distribution (LZTKD). Notably, the zero-truncated Katz distribution is a special case of this distribution. Along with the closed form expression of all its statistical characteristics, the LZTKD is proven to provide an adequate model for both underdispersed and overdispersed zero-truncated count datasets. Specifically, we show that the associated hazard rate function has increasing, decreasing, bathtub, or upside-down bathtub shapes. Moreover, we demonstrate that the LZTKD belongs to the Lagrangian distribution of the first kind. Then, applications of the LZTKD in statistical scenarios are explored. The unknown parameters are estimated using the well-reputed method of the maximum likelihood. In addition, the generalized likelihood ratio test procedure is applied to test the significance of the additional parameter. In order to evaluate the performance of the maximum likelihood estimates, simulation studies are also conducted. The use of real-life datasets further highlights the relevance and applicability of the proposed model.

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A new generalization of the zero-truncated negative binomial distribution by a Lagrange expansion with associated regression model and applications

Monisha,

Maya,

Irshad

et al. 2023

Int J Data Sci Anal

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A Novel Generalization of Zero-Truncated Binomial Distribution by Lagrangian Approach with Applications for the COVID-19 Pandemic

Cited by 3 publications

References 25 publications

A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

A Novel Flexible Class of Intervened Poisson Distribution by Lagrangian Approach

A Novel Zero-Truncated Katz Distribution by the Lagrange Expansion of the Second Kind with Associated Inferences

A new generalization of the zero-truncated negative binomial distribution by a Lagrange expansion with associated regression model and applications

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