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Journal articles on the topic 'Poisson distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 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 (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. NiÃ©rÃ©, and D. MizÃ¨re. "A Note on the (Weighted) Bivariate Poisson Distribution." European Journal of Pure and Applied Mathematics 14, no. 1 (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 Famoy

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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 (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 (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

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7

Gao, Mingchu. "Compound bi-free Poisson distributions." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 02 (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

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8

Bamigbala, Olateju Alao, Saidu S. Abdulkadir, Adesupo A. Akinrefon, and Jibasen Danjuma. "Poisson Sauleh Distribution and its Properties." International Journal of Development Mathematics (IJDM) 2, no. 2 (2025): 246–66. https://doi.org/10.62054/ijdm/0202.14.

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This study introduces the Poisson-Sauleh distribution (PSuD), a novel statistical model designed to effectively handle overdispersed and heavy-tailed count data. Traditional models, such as the Poisson and Negative Binomial distributions, often fall short in accurately modeling real-world data characterized by greater variability than the mean and heavy-tailed count data. The PSuD is a mixture of the Poisson and Sauleh distributions, while Sauleh distribution is also a mixture of Exponential and Gamma distributions, to enhance flexibility and fit for complex datasets. We derive the PSuD and ex

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9

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 (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 (

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10

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

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11

Abd El-Monsef, Mohamed, and Nora Sohsah. "POISSON TRANSMUTED LINDLEY DISTRIBUTION." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 9 (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 applicatio

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12

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 (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 s

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13

Rufin, Bidounda, Michel Koukouatikissa Diafouka, R. Ìeolie Foxie Miz Ìel Ìe Kitoti, and Dominique Miz`ere. "The Bivariate Extended Poisson Distribution of Type 1." European Journal of Pure and Applied Mathematics 14, no. 4 (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

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14

Bodhisuwan, Winai, and Sirinapa Aryuyuen. "The Poisson-Transmuted Janardan Distribution for Modelling Count Data." Trends in Sciences 19, no. 5 (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 propo

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15

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 (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 v

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16

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 (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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17

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 (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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18

Zhang, Zhehao. "A New Fractional Poisson Process Governed by a Recursive Fractional Differential Equation." Fractal and Fractional 6, no. 8 (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 proc

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19

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 (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

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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. 4 (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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21

Valero, J., M. Pérez-Casany, and J. Ginebra. "On zero-truncating and mixing Poisson distributions." Advances in Applied Probability 42, no. 04 (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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22

Kim, Hee-Young. "Applications of the Conway-Maxwell-Poisson Hidden Markov models for analyzing traffic accident." Korean Data Analysis Society 24, no. 5 (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 distrib

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23

Walhin, J. F., and J. Paris. "The Mixed Bivariate Hofmann Distribution." ASTIN Bulletin 31, no. 1 (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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24

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 (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&rsquo;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-para

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25

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 bivari

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26

Karlis, Dimitris. "EM Algorithm for Mixed Poisson and Other Discrete Distributions." ASTIN Bulletin 35, no. 01 (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 usu

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27

Karlis, Dimitris. "EM Algorithm for Mixed Poisson and Other Discrete Distributions." ASTIN Bulletin 35, no. 1 (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 usu

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28

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

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29

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

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30

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

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31

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

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32

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

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33

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

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34

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

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35

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

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36

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

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37

Dhanavanthan, P. "Compound Intervened Poisson Distribution." Biometrical Journal 40, no. 5 (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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38

Church, Kenneth W., and William A. Gale. "Poisson mixtures." Natural Language Engineering 1, no. 2 (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

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39

Rekha Radhakrishnan, D Venkatesan, and Prasanth C.B. "A New Poisson Mixture Distribution: Characterization and Biomedical Application." Bioscan 19, Special Issue-1 (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,

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40

Willmot, Gord. "Mixed Compound Poisson Distributions." ASTIN Bulletin 16, S1 (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, be

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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 probabil

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42

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 (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 identifiabilit

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43

Haridoss, V., and V. Sasikala. "Constructing Optimal Quick Switching System with Hurdle Poisson Distribution." Indian Journal Of Science And Technology 17, no. 22 (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

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44

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

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45

Vernic, Raluca. "On The Bivariate Generalized Poisson Distribution." ASTIN Bulletin 27, no. 1 (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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46

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 (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

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Oluyede, Broderick, Precious Mdlongwa, Boikanyo Makubate, and Shujiao Huang. "The Burr-Weibull Power Series Class of Distributions." Austrian Journal of Statistics 48, no. 1 (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-Rayle

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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 (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 distrib

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George, Alphonsa, and Dais George. "DISCRETIZED POISSON-EXPONENTIATED WEIBULL DISTRIBUTION AND ITS APPLICATIONS." Advances and Applications in Statistics 92, no. 3 (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-Gumbe

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

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