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Journal articles on the topic 'Poisson distribution'

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Published: 4 June 2021
Last updated: 5 July 2025

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1

Loukas, Sotirios, and H. Papageorgiou. "On a trivariate Poisson distribution." Applications of Mathematics 36, no. 6 (1991): 432–39. http://dx.doi.org/10.21136/am.1991.104480.

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2

Nganga, P. C. Batsindila, R. F. Mizelé Kitoti, E. Nguessolta, and D. Mizère. "A NOTE ON THE BIVARIATE GENERALIZED POISSON DISTRIBUTION OF TYPE 1." Far East Journal of Theoretical Statistics 69, no. 2 (April 14, 2025): 155–68. https://doi.org/10.17654/0972086325007.

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Given the univariate generalized Poisson distribution as defined by Déniz and Sarabia [5], in this paper, we construct a bivariate generalized Poisson distribution of type 1 whose marginal distributions are univariate generalized Poisson distributions according to Déniz and Sarabia [5]. We also show that this distribution belongs to the family of bivariate Poisson distributions. Under certain conditions, this distribution converges in distribution to the bivariate Poisson distribution of Berkhout and Plug [4]. It also converges to the bivariate Poisson distribution of Lakshminarayana et al. [9].
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3

Bidounga, R., P. C. Batsindila Nganga, L. Niéré, and D. Mizère. "A Note on the (Weighted) Bivariate Poisson Distribution." European Journal of Pure and Applied Mathematics 14, no. 1 (January 31, 2021): 192–203. http://dx.doi.org/10.29020/nybg.ejpam.v14i1.3895.

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In the recent statistical literature, the univariate Poisson distribution has been generalized by many authors, among them: the univariate weighted Poisson distribution [13], the generalized univariate Poisson distribution [7], the bivariate Poisson distribution according to Holgate [11], the bivariate Poisson distribution according to Lakshminarayana, Pandit and Srinivasa Rao [15], the bivariate Poisson distribution according to Berkhout and Plug [4], the bivariate weighted Poisson distribution according to Elion et al. [8] and the generalized bivariate Poisson distribution according to Famoye [9]. In this paper, We highlight the weighted bivariate Poisson distribution and show that it is the synthesis of all the bivariate Poisson distributions which, under certain conditions, converge in distribution towards the bivariate Poisson distribution according to Berkhout and Plug [4] which can be considered like the standard distribution in N2 as is the univariate Poisson distribution in N.
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4

SHANKER, Rama. "The Discrete Poisson-Aradhana Distribution." Turkiye Klinikleri Journal of Biostatistics 9, no. 1 (2017): 12–22. http://dx.doi.org/10.5336/biostatic.2017-54834.

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5

V. R., Saji Kumar. "α - Poisson Distribution". Calcutta Statistical Association Bulletin 54, № 3-4 (вересень 2003): 275–80. http://dx.doi.org/10.1177/0008068320030312.

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6

Shanker, Rama, and Kamlesh Kumar Shukla. "The Poisson-Adya distribution." Biometrics & Biostatistics International Journal 11, no. 3 (August 17, 2022): 100–103. http://dx.doi.org/10.15406/bbij.2022.11.00361.

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In this paper a Poisson mixture of Adya distribution called Poisson-Adya distribution has been suggested. The expressions of statistical constants including coefficients of variation, skewness, kurtosis and index of dispersion have been obtained and their behavior for varying values of parameter has been studied. It is observed that the obtained distribution is unimodal, has increasing hazard rate and over-dispersed. Maximum likelihood estimation and method of moment have been discussed for estimating parameter. Finally, the goodness of fit of the proposed distribution and its comparison with Poisson and Poisson-Lindley distributions has been given.
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7

Gao, Mingchu. "Compound bi-free Poisson distributions." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 02 (June 2019): 1950014. http://dx.doi.org/10.1142/s0219025719500140.

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In this paper, we study compound bi-free Poisson distributions for two-faced families of random variables. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible distribution for a two-faced family of self-adjoint random variables can be realized as the limit of a sequence of compound bi-free Poisson distributions of two-faced families of self-adjoint random variables. If a compound bi-free Poisson distribution is determined by a positive number and the distribution of a two-faced family of finitely many random variables, which has an almost sure random matrix model, and the left random variables commute with the right random variables in the two-faced family, then we can construct a random bi-matrix model for the compound bi-free Poisson distribution. If a compound bi-free Poisson distribution is determined by a positive number and the distribution of a commutative pair of random variables, we can construct an asymptotic bi-matrix model with entries of creation and annihilation operators for the compound bi-free Poisson distribution.
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8

Deshmukh, S. R., and M. S. Kasture. "BIVARIATE DISTRIBUTION WITH TRUNCATED POISSON MARGINAL DISTRIBUTIONS." Communications in Statistics - Theory and Methods 31, no. 4 (May 14, 2002): 527–34. http://dx.doi.org/10.1081/sta-120003132.

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9

Abd El-Monsef, Mohamed, and Nora Sohsah. "POISSON TRANSMUTED LINDLEY DISTRIBUTION." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 9 (January 1, 2016): 5631–38. http://dx.doi.org/10.24297/jam.v11i9.816.

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The main purpose of this paper is to introduce a new discrete compound distribution, namely Poisson Transmuted Lindley distribution (PTL) which offers a more flexible model for analyzing some types of countable data. The proposed distribution is accommodate unimodel, bathtub as well as decreasing failure rates. Most of the statistical and reliability measures are derived. For the estimation purposes the method of moment and maximum likelihood methods are studied for PTL. Simulation studies are conducted to investigate the performance of the maximum likelihood estimators. A real life application for PTL is introduced to test its goodness of fit and examine its performance compared with some other distributions.
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10

Shanker, Rama, and Kamlesh Kumar Shukla. "A new three-parameter size-biased poisson-lindley distribution with properties and applications." Biometrics & Biostatistics International Journal 9, no. 1 (February 11, 2020): 1–4. http://dx.doi.org/10.15406/bbij.2020.09.00294.

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A new three-parameter size-biased Poisson-Lindley distribution which includes several one parameter and two-parameter size-biased distributions including size-biased geometric distribution (SBGD), size-biased negative binomial distribution (SBNBD), size-biased Poisson-Lindley distribution (SBPLD), size-biased Poisson-Shanker distribution (SBPSD), size-biased two-parameter Poisson-Lindley distribution-1 (SBTPPLD-1), size-biased two-parameter Poisson-Lindley distribution-2(SBTPPLD-2), size-biased quasi Poisson-Lindley distribution (SBQPLD) and size-biased new quasi Poisson-Lindley distribution (SBNQPLD) for particular cases of parameters has been proposed. Its various statistical properties based on moments including coefficient of variation, skewness, kurtosis and index of dispersion have been studied. Maximum likelihood estimation has been discussed for estimating the parameters of the distribution. Goodness of fit of the proposed distribution has been discussed.
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11

Sormin, Corry, Gusmanely Z, and Nurhidayah Nurhidayah. "Generalized Poisson Regression Type-II at Jambi City Health Office." Eksakta : Berkala Ilmiah Bidang MIPA 21, no. 1 (April 30, 2020): 54–58. http://dx.doi.org/10.24036/eksakta/vol21-iss1/222.

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One statistical analysis is regression analysis. One regression that has the assumption of poisson distribution is poisson regression which has the assumption of poisson distribution. Neonatal deaths are still very rare, so the proper analysis is used, namely Generalized Poisson Regression. This regression method is specifically used for Poissson distributed data. The stages that will be carried out in this research are Poisson distribution test and equidispersion assumption, parameter estimation, model feasibility test and best model selection. Data from the Jambi City Health Office in 2018 showed that the Generalized Poisson Regression regression alleged had a variable number of first trimester visits, the number of pregnant women getting Tetanus Diptheria immunization, the estimated number of neonatal infants with complications, the number of infants receiving Hepatitis B immunization was less than twenty-four hours, the number of infants receiving BCG immunizations.
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12

Rufin, Bidounda, Michel Koukouatikissa Diafouka, R. Ìeolie Foxie Miz Ìel Ìe Kitoti, and Dominique Miz`ere. "The Bivariate Extended Poisson Distribution of Type 1." European Journal of Pure and Applied Mathematics 14, no. 4 (November 10, 2021): 1517–29. http://dx.doi.org/10.29020/nybg.ejpam.v14i4.4151.

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In this paper, we will construct the bivariate extended Poisson distribution whichgeneralizes the univariate extended Poisson distribution. This law will be obtained by the method of the product of its marginal laws by a factor. This method was demonstrated in [7]. Thus we call the bivariate extended Poisson distribution of type 1 the bivariate extended Poisson distribution obtained by the method of the product of its marginal distributions by a factor. We will show that this distribution belongs to the family of bivariate Poisson distributions and and will highlight the conditions relating to the independence of the marginal variables. A simulation study was realised.
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13

Bodhisuwan, Winai, and Sirinapa Aryuyuen. "The Poisson-Transmuted Janardan Distribution for Modelling Count Data." Trends in Sciences 19, no. 5 (February 25, 2022): 2898. http://dx.doi.org/10.48048/tis.2022.2898.

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In this paper, we introduce a new mixed Poisson distribution, called the Poisson-transmuted Janardan distribution. The Poisson-Janardan and Poisson-Lindley distributions are sub-model of the proposed distribution. Some mathematical properties of the proposed distribution, including the moments, moment generating function, probability generating function and generation of a Poisson-transmuted Janardan random variable, are presented. The parameter estimation is discussed based on the method of moments and the maximum likelihood estimation. In addition, we illustrated the application of the proposed distribution by fitting with 4 real data sets and comparing it with some other distributions based on the Kolmogorov-Smirnov test for criteria.
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14

Thavaneswaran, Aerambamoorthy, Saumen Mandal, and Dharini Pathmanathan. "Estimation for Wrapped Zero Inflated Poisson and Wrapped Poisson Distributions." International Journal of Statistics and Probability 5, no. 3 (April 8, 2016): 1. http://dx.doi.org/10.5539/ijsp.v5n3p1.

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There has been a growing interest in discrete circular models such as wrapped zero inflated Poisson and wrapped Poisson distributions and the trigonometric moments (see Brobbey et al., 2016 and Girija et al., 2014). Also, characteristic functions of stable processes have been used to study the estimation of the model parameters using estimating function approach (see Thavaneswaran et al., 2013). One difficulty in estimating the circular mean and the resultant mean length parameter of wrapped Poisson (WP) or wrapped zero inflated Poisson (WZIP) is that neither the likelihood of WP/WZIP random variable nor the score function is available in closed form, which leads one to use either trigonometric method of moment estimation (TMME) or an estimating function approach. In this paper, we study the estimation of WZIP distribution and WP distribution using estimating functions and obtain the closed form expression of the information matrix. We also derive the asymptotic distribution of the tangent of the mean direction for both the WZIP and WP distributions.
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15

Louzayadio, C. G., E. Nguessolta, M. Koukouatikissa Diafouka, R. Bidounga, and D. Mizère. "THE BIVARIATE EXTENDED POISSON DISTRIBUTION OF TYPE 2." Journal of Computer Science and Applied Mathematics 5, no. 2 (October 10, 2023): 89–102. http://dx.doi.org/10.37418/jcsam.5.2.4.

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In this paper we undertake the construction of a bivariate distribution generalising the univariate extended Poisson distribution by using the method of crossing laws, a method highlighted in [7]. We will call this law "the bivariate extended Poisson distribution of type 2", in reference to "the bivariate extended Poisson law of type 1" highlighted in [4]. We have shown that this law is a member of the family of bivariate Poisson distributions. Functional relations will be established between the two distributions.
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16

ARRATIA, RICHARD, A. D. BARBOUR, and SIMON TAVARÉ. "The Poisson–Dirichlet Distribution and the Scale-Invariant Poisson Process." Combinatorics, Probability and Computing 8, no. 5 (September 1999): 407–16. http://dx.doi.org/10.1017/s0963548399003910.

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We show that the Poisson–Dirichlet distribution is the distribution of points in a scale-invariant Poisson process, conditioned on the event that the sum T of the locations of the points in (0,1] is 1. This extends to a similar result, rescaling the locations by T, and conditioning on the event that T[les ]1. Restricting both processes to (0, β] for 0<β[les ]1, we give an explicit formula for the total variation distance between their distributions. Connections between various representations of the Poisson–Dirichlet process are discussed.
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17

Zhang, Zhehao. "A New Fractional Poisson Process Governed by a Recursive Fractional Differential Equation." Fractal and Fractional 6, no. 8 (July 29, 2022): 418. http://dx.doi.org/10.3390/fractalfract6080418.

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This paper proposes a new fractional Poisson process through a recursive fractional differential governing equation. Unlike the homogeneous Poison process, the Caputo derivative on the probability distribution of k jumps with respect to time is linked to all probability distribution functions of j jumps, where j is a non-negative integer less than or equal to k. The distribution functions of arrival times are derived, while the inter-arrival times are no longer independent and identically distributed. Further, this new fractional Poisson process can be interpreted as a homogeneous Poisson process whose natural time flow has been randomized, and the underlying time randomizing process has been studied. Finally, the conditional distribution of the kth order statistic from random number samples, counted by this fractional Poisson process, is also discussed.
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18

Al-obedy, Jinan A. Naser. "Posterior Estimates for the Parameter of the Poisson Distribution by Using Two Different Loss Functions." Ibn AL- Haitham Journal For Pure and Applied Sciences 35, no. 1 (January 20, 2022): 60–72. http://dx.doi.org/10.30526/35.1.2800.

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In this paper, Bayes estimators of Poisson distribution have been derived by using two loss functions: the squared error loss function and the proposed exponential loss function in this study, based on different priors classified as the two different informative prior distributions represented by erlang and inverse levy prior distributions and non-informative prior for the shape parameter of Poisson distribution. The maximum likelihood estimator (MLE) of the Poisson distribution has also been derived. A simulation study has been fulfilled to compare the accuracy of the Bayes estimates with the corresponding maximum likelihood estimate (MLE) of the Poisson distribution based on the root mean squared error (RMSE) for different cases of the parameter of the Poisson distribution and different sample sizes.
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19

Valero, J., M. Pérez-Casany, and J. Ginebra. "On zero-truncating and mixing Poisson distributions." Advances in Applied Probability 42, no. 4 (December 2010): 1013–27. http://dx.doi.org/10.1239/aap/1293113149.

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The distributions that result from zero-truncating mixed Poisson (ZTMP) distributions and those obtained from mixing zero-truncated Poisson (MZTP) distributions are characterised based on their probability generating functions. One consequence is that every ZTMP distribution is an MZTP distribution, but not vice versa. These characterisations also indicate that the size-biased version of a Poisson mixture and, under certain regularity conditions, the shifted version of a Poisson mixture are neither ZTMP distributions nor MZTP distributions.
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20

Valero, J., M. Pérez-Casany, and J. Ginebra. "On zero-truncating and mixing Poisson distributions." Advances in Applied Probability 42, no. 04 (December 2010): 1013–27. http://dx.doi.org/10.1017/s000186780000450x.

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The distributions that result from zero-truncating mixed Poisson (ZTMP) distributions and those obtained from mixing zero-truncated Poisson (MZTP) distributions are characterised based on their probability generating functions. One consequence is that every ZTMP distribution is an MZTP distribution, but not vice versa. These characterisations also indicate that the size-biased version of a Poisson mixture and, under certain regularity conditions, the shifted version of a Poisson mixture are neither ZTMP distributions nor MZTP distributions.
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21

Kim, Hee-Young. "Applications of the Conway-Maxwell-Poisson Hidden Markov models for analyzing traffic accident." Korean Data Analysis Society 24, no. 5 (October 31, 2022): 1655–65. http://dx.doi.org/10.37727/jkdas.2022.24.5.1655.

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This paper documents the application of the Conway-Maxwell-Poisson(CMP) hidden Markov model for modelling motor vehicle crashes. The CMP distribution is a twoparameter extension of the Poisson distribution that generalizes some well-known discrete distributions(Poisson, Bernoulli and geometric). Also it leads to the generalizations of distributions derived from theses discrete distributions, that is, the binomial and negative binomial distributions. The advantage of CMP distribution is its ability to handle both under and over-dispersion through controlling one special parameter in the distribution, which makes it more flexible than Poisson distribution. We consider the data consisting of the daily number of injuries on the road in 2020 from the TAAS(Traffic Accident Analysis System). We apply CMP hidden Markov model to data, the parameters are estimated via maximim likelihood, and find that this model achieves better performance than commonly used Poisson hidden Markov model. For the decoding procedure, the Viterbi algorithm is implemented.
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22

Walhin, J. F., and J. Paris. "The Mixed Bivariate Hofmann Distribution." ASTIN Bulletin 31, no. 1 (May 2001): 123–38. http://dx.doi.org/10.2143/ast.31.1.997.

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AbstractIn this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case.We show how to evaluate the bivariate aggregate claims distribution and we fit some insurance portfolios given in the literature.This study typically extends the use of the Bivariate Independent Poisson Distribution, the Mixed Bivariate Negative Binomial and the Mixed Bivariate Poisson Inverse Gaussian Distribution.
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23

Gelin Louzayadio, Chedly, Rodnellin Onesime Malouata, and Michel Diafouka Koukouatikissa. "A Weighted Poisson Distribution for Underdispersed Count Data." International Journal of Statistics and Probability 10, no. 4 (June 28, 2021): 157. http://dx.doi.org/10.5539/ijsp.v10n4p157.

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In this paper, we present a new weighted Poisson distribution for modeling underdispersed count data. Weighted Poisson distribution occurs naturally in contexts where the probability that a particular observation of Poisson variable enters the sample gets multiplied by some non-negative weight function. Suppose a realization y of Y a Poisson random variable enters the investigator’s record with probability proportional to w(y): Clearly, the recorded y is not an observation on Y, but on the random variable Yw, which is said to be the weighted version of Y. This distribution a two-parameter is from the exponential family, it includes and generalizes the Poisson distribution by weighting. It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000). We present some moment properties and we estimate its parameters. One classical example is considered to compare the fits of this new distribution with the extended Poisson distribution.
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24

Mohammed, B. I., Abdulaziz S. Alghamdi, Hassan M. Aljohani, and Md Moyazzem Hossain. "The Novel Bivariate Distribution: Statistical Properties and Real Data Applications." Mathematical Problems in Engineering 2021 (December 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/2756779.

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This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.
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25

Fatima, Anum, and Ayesha Roohi. "Extended Poisson Exponential Distribution." Pakistan Journal of Statistics and Operation Research 11, no. 3 (September 8, 2015): 361. http://dx.doi.org/10.18187/pjsor.v11i3.708.

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26

J. Priyadharshini, and V. Saavithri. "Com-Poisson Thomas Distribution." International Journal of Research in Advent Technology 7, no. 1 (February 10, 2019): 238–44. http://dx.doi.org/10.32622/ijrat.71201922.

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27

Mahmoudi, E., and H. Zakerzadeh. "Generalized Poisson–Lindley Distribution." Communications in Statistics - Theory and Methods 39, no. 10 (May 12, 2010): 1785–98. http://dx.doi.org/10.1080/03610920902898514.

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28

Chandra, Nimai Kumar, Dilip Roy, and Tirthankar Ghosh. "A Generalized Poisson Distribution." Communications in Statistics - Theory and Methods 42, no. 15 (August 3, 2013): 2786–97. http://dx.doi.org/10.1080/03610926.2011.620207.

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29

Bakouch, Hassan S., Maher Kachour, and Saralees Nadarajah. "An extended Poisson distribution." Communications in Statistics - Theory and Methods 45, no. 22 (January 25, 2016): 6746–64. http://dx.doi.org/10.1080/03610926.2014.967587.

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30

Karuppusamy, Sadasivan. "IMPROVED POISSON-LINDLEY DISTRIBUTION." Advances and Applications in Statistics 65, no. 1 (November 20, 2020): 57–68. http://dx.doi.org/10.17654/as065010057.

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31

Al-Zahrani, Bander, and Hanaa Sagor. "The Poisson-Lomax Distribution." Revista Colombiana de Estadística 37, no. 1 (July 9, 2014): 225. http://dx.doi.org/10.15446/rce.v37n1.44369.

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32

Leask, Kerry L., and Linda M. Haines. "The Altham–Poisson distribution." Statistical Modelling: An International Journal 15, no. 5 (February 11, 2015): 476–97. http://dx.doi.org/10.1177/1471082x15571161.

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33

Farnsworth, David L. "Scaling the Poisson Distribution." PRIMUS 24, no. 2 (January 17, 2014): 104–15. http://dx.doi.org/10.1080/10511970.2013.842191.

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34

Dhanavanthan, P. "Compound Intervened Poisson Distribution." Biometrical Journal 40, no. 5 (September 1998): 641–46. http://dx.doi.org/10.1002/(sici)1521-4036(199809)40:5<641::aid-bimj641>3.0.co;2-f.

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35

Church, Kenneth W., and William A. Gale. "Poisson mixtures." Natural Language Engineering 1, no. 2 (June 1995): 163–90. http://dx.doi.org/10.1017/s1351324900000139.

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AbstractShannon (1948) showed that a wide range of practical problems can be reduced to the problem of estimating probability distributions of words and ngrams in text. It has become standard practice in text compression, speech recognition, information retrieval and many other applications of Shannon's theory to introduce a “bag-of-words” assumption. But obviously, word rates vary from genre to genre, author to author, topic to topic, document to document, section to section, and paragraph to paragraph. The proposed Poisson mixture captures much of this heterogeneous structure by allowing the Poisson parameter θ to vary over documents subject to a density function φ. φ is intended to capture dependencies on hidden variables such genre, author, topic, etc. (The Negative Binomial is a well-known special case where φ is a Г distribution.) Poisson mixtures fit the data better than standard Poissons, producing more accurate estimates of the variance over documents (σ2), entropy (H), inverse document frequency (IDF), and adaptation (Pr(x ≥ 2/x ≥ 1)).
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36

Karlis, Dimitris. "EM Algorithm for Mixed Poisson and Other Discrete Distributions." ASTIN Bulletin 35, no. 01 (May 2005): 3–24. http://dx.doi.org/10.2143/ast.35.1.583163.

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Mixed Poisson distributions are widely used in various disciplines including actuarial applications. The family of mixed Poisson distributions contains several members according to the choice of the mixing distribution for the parameter of the Poisson distribution. Very few of them have been studied in depth, mainly because of algebraic intractability. In this paper we will describe an EM type algorithm for maximum likelihood estimation for mixed Poisson distributions. The main achievement is that it reduces the problem of estimation to one of estimation of the mixing distribution which is usually easier. Variants of the algorithm work even when the probability function of the mixed distribution is not known explicitly but we have only an approximation of it. Other discrete distributions are treated as well.
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37

Karlis, Dimitris. "EM Algorithm for Mixed Poisson and Other Discrete Distributions." ASTIN Bulletin 35, no. 1 (May 2005): 3–24. http://dx.doi.org/10.1017/s0515036100014033.

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Mixed Poisson distributions are widely used in various disciplines including actuarial applications. The family of mixed Poisson distributions contains several members according to the choice of the mixing distribution for the parameter of the Poisson distribution. Very few of them have been studied in depth, mainly because of algebraic intractability. In this paper we will describe an EM type algorithm for maximum likelihood estimation for mixed Poisson distributions. The main achievement is that it reduces the problem of estimation to one of estimation of the mixing distribution which is usually easier. Variants of the algorithm work even when the probability function of the mixed distribution is not known explicitly but we have only an approximation of it. Other discrete distributions are treated as well.
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38

Rekha Radhakrishnan, D Venkatesan, and Prasanth C.B. "A New Poisson Mixture Distribution: Characterization and Biomedical Application." Bioscan 19, Special Issue-1 (December 28, 2024): 928–35. https://doi.org/10.63001/tbs.2024.v19.i02.s.i(1).pp928-935.

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This study presents a novel Poisson mixture distribution, combining elements of the Poisson and Suja distributions. The structural properties of this distribution are derived, including the formulation of the r-th central moments. Additionally, formulas for the coefficient of variation, skewness, and kurtosis are provided, with their behaviors illustrated through graphical representations. Key statistical properties, such as the hazard rate function and generating functions, are also discussed. Methods for parameter estimation, including maximum likelihood estimation and the method of moments, are explored. A simulation study has been conducted to assess the model. In many practical scenarios, real-world datasets do not fit well with conventional distributions. In this case, a dataset of newborn babies' weights from a hospital in Kerala over a specific period is analyzed, focusing on the number of newborns with critically low birth weight (Extremely Low Birth Weight, or ELBW). This data is fitted using the Poisson-Suja distribution. The goodness of fit of the proposed distribution is demonstrated using the count dataset, showing it outperforms the Poisson, Poisson Lindley (PL), and Poisson Akash (PA) distributions.
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39

Willmot, Gord. "Mixed Compound Poisson Distributions." ASTIN Bulletin 16, S1 (April 1986): S59—S79. http://dx.doi.org/10.1017/s051503610001165x.

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AbstractThe distribution of total claims payable by an insurer is considered when the frequency of claims is a mixed Poisson random variable. It is shown how in many cases the total claims density can be evaluated numerically using simple recursive formulae (discrete or continuous).Mixed Poisson distributions often have desirable properties for modelling claim frequencies. For example, they often have thick tails which make them useful for long-tailed data. Also, they may be interpreted as having arisen from a stochastic process. Mixing distributions considered include the inverse Gaussian, beta, uniform, non-central chi-squared, and the generalized inverse Gaussian as well as other more general distributions.It is also shown how these results may be used to derive computational formulae for the total claims density when the frequency distribution is either from the Neyman class of contagious distributions, or a class of negative binomial mixtures. Also, a computational formula is derived for the probability distribution of the number in the system for the M/G/1 queue with bulk arrivals.
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40

Irshad, Muhammed Rasheed, Christophe Chesneau, Damodaran Santhamani Shibu, Mohanan Monisha, and Radhakumari Maya. "Lagrangian Zero Truncated Poisson Distribution: Properties Regression Model and Applications." Symmetry 14, no. 9 (August 25, 2022): 1775. http://dx.doi.org/10.3390/sym14091775.

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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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41

Sah, Binod Kumar, and A. Mishra. "A Generalised Exponential-Lindley Mixture of Poisson Distribution." Nepalese Journal of Statistics 3 (September 11, 2019): 11–20. http://dx.doi.org/10.3126/njs.v3i0.25575.

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Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD.&#x0D; Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution.&#x0D; Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970).&#x0D; Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.
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42

Haridoss, V., and V. Sasikala. "Constructing Optimal Quick Switching System with Hurdle Poisson Distribution." Indian Journal Of Science And Technology 17, no. 22 (June 3, 2024): 2296–304. http://dx.doi.org/10.17485/ijst/v17i22.581.

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Objectives: Optimizing the sum of risks involved in the selection of acceptance sampling plans playing a vital role. This paper uses the Hurdle Poisson distribution to design an optimal quick switching system attribute plan for a given acceptable quality level (AQL) and limiting quality level (LQL) involving a minimum sum of risks. Methods: The sum of producer's and consumer's risks has been met for the specified AQL and LQL. The sum of these risks, as well as the acceptance and rejection numbers have been calculated using the Hurdle Poisson distribution. The operating characteristic function for the quick switching system attribute plan has also been derived using the Hurdle Poisson distribution. Findings: The producer and the consumer both represent the same party in the final inspection. As a result, the sum of these two risks should be minimized. In this paper, the sum of risks for various operating ratios are tabulated using the Hurdle Poisson distribution. These tabulated values are less than the sum of risks calculated using the Weighted Poisson distribution. Novelty: Reducing the sum of risks is the ultimate aim of the work. In this proposed paper, to attain the minimum sum of risks, the authors make an attempt to approach the Quick Switching System Sampling Plan, when the number of defectives in the submitted lots are very less. In other words, the probability of getting defective is very less. This indicates the quality of the lot selected for the inspection to ensure the protection for the consumer. And the plan is also designed in the way that the producer is also not get affected by rejecting a good lot by the consumer. This is the requirement of minimizing the risks. Keywords: Acceptable Quality Level (AQL), Limiting Quality Level (LQL), Minimum Risk Plan, Quick Switching System Sampling Attribute Plan, Operating Characteristic (OC) Function, Hurdle Poisson Distribution
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43

Pudovkin, Alexander I., and Lutz Bornmann. "Approximation of citation distributions to the Poisson distribution." COLLNET Journal of Scientometrics and Information Management 12, no. 1 (January 2, 2018): 49–53. http://dx.doi.org/10.1080/09737766.2017.1332605.

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44

Vernic, Raluca. "On The Bivariate Generalized Poisson Distribution." ASTIN Bulletin 27, no. 1 (May 1997): 23–32. http://dx.doi.org/10.2143/ast.27.1.542065.

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AbstractThis paper deals with the bivariate generalized Poisson distribution. The distribution is fitted to the aggregate amount of claims for a compound class of policies submitted to claims of two kinds whose yearly frequencies are a priori dependent. A comparative study with the bivariate Poisson distribution and with two bivariate mixed Poisson distributions has been carried out, based on data concerning natural events insurance in the USA and third party liability automobile insurance in France.
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45

MEINTANIS, SIMOS, and I. A. KOUTROUVELIS. "TESTING THE FIT TO GENERALIZED POISSON DISTRIBUTIONS BASED ON AN EMPIRICAL TRANSFORM." International Journal of Reliability, Quality and Safety Engineering 08, no. 01 (March 2001): 59–76. http://dx.doi.org/10.1142/s0218539301000359.

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Generalized Poisson distributions appear as applied-research models in many fields. For example in reliability, the total amount of wear of items, the hazard rate and the total time to failure can be modeled after a Generalized Poisson distribution. Methods of Statistical Inference for such distributions have been scarce since the corresponding distribution functions come in complicated, often not closed form, expressions. In this article, we present a method for testing the goodness-of-fit to any specified member of the family of Generalized Poisson distributions. The proposed method utilizes the general form of the moment generating function of Generalized Poisson distributions. The asymptotic distribution of the test statistics is derived when the parameters of the generalizing distribution are assumed known as well as unknown. The performance of the procedures is investigated by employing real and simulated data.
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46

Oluyede, Broderick, Precious Mdlongwa, Boikanyo Makubate, and Shujiao Huang. "The Burr-Weibull Power Series Class of Distributions." Austrian Journal of Statistics 48, no. 1 (December 17, 2018): 1–13. http://dx.doi.org/10.17713/ajs.v48i1.633.

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A new generalized class of distributions called the Burr-Weibull Power Series (BWPS) class of distributions is developed and explored. This class of distributions generalizes the Burr power series and Weibull power series classes of distributions, respectively. A special model of the BWPS class of distributions, the new Burr-Weibull Poisson (BWP) distribution is considered and some of its mathematical properties are obtained. The BWP distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential Poisson, Burr-exponential, Burr-Rayleigh Poisson, Burr-Rayleigh, Burr-Poisson, Burr, Lomax-exponential Poisson, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax-Poisson, Lomax, Weibull, Rayleigh and exponential distributions. Maximum likelihood estimation technique is used to estimate the model parameters followed by a Monte Carlo simulation study. Finally an application of the BWP model to a real data set is presented to illustrate the usefulness of the proposed class of distributions.
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47

Ayo, Ayenigba Alfred, Amoyedo Femi Emmanuel, and Afariogun David Adebisi. "The Binosson Distribution: A Unified Probabilistic Framework Bridging the Binomial and Poisson Models." Mikailalsys Journal of Mathematics and Statistics 3, no. 2 (April 7, 2025): 343–53. https://doi.org/10.58578/mjms.v3i2.5318.

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Classical Binomial and Poisson distributions, constrained by fixed trials and static event rates, falter in modeling modern datasets with dynamic parameters or contextual dependencies (e.g., variable infection rates, covariate-influenced risks). This paper introduces the Binosson Distribution, a hybrid framework unifying Binomial trials and Poisson processes through dynamic parameterization of trial counts (n) and designed to address event rates (λ). The distribution has been proposed to bridge the gap between these two distributions, incorporating aspects of both. Binomial-cum-Poisson distributions are modified to obtain a distribution that will be able to solve the probability problems that lies between the two distributions. Binosson is the result from the product of Binomial and Poisson distributions. Statistical properties such as mean, variance, standard deviation, skewedness and kurtosis were also derived.
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48

George, Alphonsa, and Dais George. "DISCRETIZED POISSON-EXPONENTIATED WEIBULL DISTRIBUTION AND ITS APPLICATIONS." Advances and Applications in Statistics 92, no. 3 (February 17, 2025): 449–70. https://doi.org/10.17654/0972361725020.

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In this article, a discretized form of Poisson-exponentiated Weibull distribution namely, discrete Poisson exponentiated Weibull (DPEW) distribution is introduced and studied. The model parameters are estimated using the method of maximum likelihood and its accuracy is established through simulated data. The adequacy of the new distribution in modelling count datasets, in comparison to alternative distributions, is demonstrated with different real datasets of asymmetric nature. A bivariate form of discrete Poisson-exponentiated Weibull distribution is also developed by considering Farlie-Gumbel-Morgenstern copula.
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49

Shimizu, Eiji, and Hiroshi Shiraishi. "An asymptotic distribution of compound Poisson distribution." Cogent Mathematics 3, no. 1 (August 29, 2016): 1221614. http://dx.doi.org/10.1080/23311835.2016.1221614.

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50

Bening, Vladimir, and Victor Korolev. "Comparing Compound Poisson Distributions by Deficiency: Continuous-Time Case." Mathematics 10, no. 24 (December 12, 2022): 4712. http://dx.doi.org/10.3390/math10244712.

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In the paper, we apply a new approach to the comparison of the distributions of sums of random variables to the case of Poisson random sums. This approach was proposed in our previous work (Bening, Korolev, 2022) and is based on the concept of statistical deficiency. Here, we introduce a continuous analog of deficiency. In the case under consideration, by continuous deficiency, we will mean the difference between the parameter of the Poisson distribution of the number of summands in a Poisson random sum and that of the compound Poisson distribution providing the desired accuracy of the normal approximation. This approach is used for the solution of the problem of determination of the distribution of a separate term in the Poisson sum that provides the least possible value of the parameter of the Poisson distribution of the number of summands guaranteeing the prescribed value of the (1−α)-quantile of the normalized Poisson sum for a given α∈(0,1). This problem is solved under the condition that possible distributions of random summands possess coinciding first three moments. The approach under consideration is applied to the collective risk model in order to determine the distribution of insurance payments providing the least possible time that provides the prescribed Value-at-Risk. This approach is also used for the problem of comparison of the accuracy of approximation of the asymptotic (1−α)-quantile of the sum of independent, identically distributed random variables with that of the accompanying infinitely divisible distribution.
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