On Finite Mixtures of Modified Intervened Poisson Distribution And Its Applications

Kumar, C. Satheesh; Shibu, Damodaran Santhamani

doi:10.2991/jsta.2014.13.4.7

Cited by 5 publications

(7 citation statements)

References 10 publications

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“…In view of the applications of the DLF configured with the function f 1 (z) in (5), it is motivating to explore a new horizon of distribution with the choice of a new function f 2 (z).…”

Section: Importance Of the Lagrangian Familymentioning

confidence: 99%

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Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications

et al. 2022

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In this paper, we construct a new Lagrangian discrete distribution, named the Lagrangian zero truncated Poisson distribution (LZTPD). It can be presented as a generalization of the zero truncated Poissson distribution (ZTPD) and an alternative to the intervened Poisson distribution (IPD), which was elaborated for modelling both over-dispersed and under-dispersed count datasets. The mathematical aspects of the LZTPD are thoroughly investigated, and its connection to other discrete distributions is crucially observed. Further, we define a finite mixture of LZTPDs and establish its identifiability condition along with some distributional aspects. Statistical work is then performed. The maximum likelihood and method of moment approaches are used to estimate the unknown parameters of the LZTPD. Simulation studies are also undertaken as an assessment of the long-term performance of the estimates. The significance of one additional parameter in the LZTPD is tested using a generalized likelihood ratio test. Moreover, we propose a new count regression model named the Lagrangian zero truncated Poisson regression model (LZTPRM) and its parameters are estimated by the maximum likelihood estimation method. Two real-world datasets are considered to demonstrate the LZTPD’s real-world applicability, and healthcare data are analyzed to demonstrate the LZTPRM’s superiority.

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“…In view of the applications of the DLF configured with the function f 1 (z) in (5), it is motivating to explore a new horizon of distribution with the choice of a new function f 2 (z).…”

Section: Importance Of the Lagrangian Familymentioning

confidence: 99%

“…Ref. [5] considered a modified version of the IPD which has an advantage over the IPD in stretching the probability in all directions so that clustering of probabilities at initial values of the operating mechanism is overlooked. Ref.…”

Section: Introductionmentioning

confidence: 99%

Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications

et al. 2022

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“…with Z G (s) as the pgf of Z. Result 2.3 The mean and variance of EIGD is Mean = 1+δ1 + δ2 +m δ3 (9) and Variance = δ1(1+ δ1)+δ2(1+ δ2)+m 2 δ3(1+δ3) (10) where δ j for j=1,2,3 are as defined in Result 2.2. Proof: On differentiating the pgf G z (s) of "Z" given in equation 3with respect to s and putting s=1, we get…”

Section: Extended Intervened Geometric Distributionmentioning

confidence: 99%

“…The intervened type distributions such as intervened Poisson distribution (IPD), intervened geometric distribution (IGD) and modified intervened geometric distribution (MIGD) has been studied by several authors. For example see Shanmugan [1,2], Huang and Fung [3], Scollink [4], Dhanavanthan [5,6], Kumar and Shibu [7][8][9][10][11][12][13][14][15], Bartolucci et al [16], Kumar and Sreeja [17] etc.…”

Section: Introductionmentioning

confidence: 99%

Extended Intervened Geometric Distribution

Kumar¹

2016

IJSDA

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Here we develop an extended version of the modified intervened geometric distribution of Kumar and Sreeja (The Aligarh Journal of Statistics, 2014) and investigate some of its important statistical properties. Parameters of the distribution are estimated by various methods of estimation such as the method of factorial moments, the method of mixed moments and the method of maximum likelihood. The distribution has been fitted to a real life data set for illustrating its practical relevance.

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“…Kumar and Shibu (2011) modified the IPD in order to incorporate the situation of further intervention and Kumar and Shibu (2012) obtained alternative form of the truncated IPD. Further, Kumar and Shibu (2014) propose mixture of intervened poisson distribution. Also Kumar and Sreejakumari (2012) develop intervened negative binomial distribution and studied its property.…”

Section: Introductionmentioning

confidence: 99%

An Extension of Poisson Distribution and its Applications in Human Reproduction

Singh¹,

Shukla²

2021

Journal of Data Science

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An extension of truncated Poisson distribution having two parameters for a group of two types of population is derived and named as Bounded Poisson (BP) distribution. To estimate the parameters, method of moment has been employed. To check the suitability and applicability of the model it has been applied on real data set on human fertility derived from the third round of National Family Health Survey conducted in 2005-06 in Uttar Pradesh, India. Proposed model provides a good fitting to the data under consideration.

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On Finite Mixtures of Modified Intervened Poisson Distribution And Its Applications

Cited by 5 publications

References 10 publications

Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications

Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications

Extended Intervened Geometric Distribution

An Extension of Poisson Distribution and its Applications in Human Reproduction

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