Academic literature on the topic 'Multinomial distribution'

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Journal articles on the topic "Multinomial distribution"

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Roos, Bero, and Bero Roos. "Multinomial and Krawtchouk Approximations to the Generalized Multinomial Distribution." Teoriya Veroyatnostei i ee Primeneniya 46, no. 1 (2001): 117–33. http://dx.doi.org/10.4213/tvp3954.

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Roos, B. "Multinomial and Krawtchouk Approximations to the Generalized Multinomial Distribution." Theory of Probability & Its Applications 46, no. 1 (January 2002): 103–17. http://dx.doi.org/10.1137/s0040585x97978750.

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Gupta, A. K., and S. G. Lindle. "Multinomial Distribution and Ascertainment Models." Biometrical Journal 27, no. 6 (1985): 691–95. http://dx.doi.org/10.1002/bimj.4710270614.

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Dinh, Khoan T., Truc T. Nguyen, and Yining Wang. "Characterizations of multinomial distributions based on conditional distributions." International Journal of Mathematics and Mathematical Sciences 19, no. 3 (1996): 595–602. http://dx.doi.org/10.1155/s0161171296000828.

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ACZEL, AMIR D., DOMINIQUE M. A. HAUGHTON, and NORMAN H. JOSEPHY. "Ross Perot and the Multinomial Distribution." Communication Research 21, no. 3 (June 1994): 408–18. http://dx.doi.org/10.1177/009365094021003010.

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Vágó, Emese, Sándor Kemény, and Zsolt Láng. "Overdispersion at the Binomial and Multinomial Distribution." Periodica Polytechnica Chemical Engineering 55, no. 1 (2011): 17. http://dx.doi.org/10.3311/pp.ch.2011-1.03.

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Yuan, Demei, and Jianhua Zheng. "Conditionally negative association resulting from multinomial distribution." Statistics & Probability Letters 83, no. 10 (October 2013): 2222–27. http://dx.doi.org/10.1016/j.spl.2013.06.004.

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Burks, Robert E. "Jelly Belly Mixing and Uniform Multinomial Distribution." CHANCE 24, no. 1 (January 2011): 24–28. http://dx.doi.org/10.1080/09332480.2011.10739848.

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Berry, Kenneth J., and Paul W. Mielke. "Exact Cumulative Probabilities for the Multinomial Distribution." Educational and Psychological Measurement 55, no. 5 (October 1995): 769–72. http://dx.doi.org/10.1177/0013164495055005008.

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Davis, Charles S., and Michael P. Jones. "Maximum Likelihood Estimation: for the Multinomial Distribution." Teaching Statistics 14, no. 3 (September 1992): 9–11. http://dx.doi.org/10.1111/j.1467-9639.1992.tb00231.x.

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Dissertations / Theses on the topic "Multinomial distribution"

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Frühwirth-Schnatter, Sylvia, and Rudolf Frühwirth. "Bayesian Inference in the Multinomial Logit Model." Austrian Statistical Society, 2012. http://epub.wu.ac.at/5629/1/186%2D751%2D1%2DSM.pdf.

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The multinomial logit model (MNL) possesses a latent variable representation in terms of random variables following a multivariate logistic distribution. Based on multivariate finite mixture approximations of the multivariate logistic distribution, various data-augmented Metropolis-Hastings algorithms are developed for a Bayesian inference of the MNL model.
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Olteanu, Denisa Anca. "Cumulative Sum Control Charts for Censored Reliability Data." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/26665.

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Companies routinely perform life tests for their products. Typically, these tests involve running a set of products until the units fail. Most often, the data are censored according to different censoring schemes, depending on the particulars of the test. On occasion, tests are stopped at a predetermined time and the units that are yet to fail are suspended. In other instances, the data are collected through periodic inspection and only upper and lower bounds on the lifetimes are recorded. Reliability professionals use a number of non-normal distributions to model the resulting lifetime data with the Weibull distribution being the most frequently used. If one is interested in monitoring the quality and reliability characteristics of such processes, one needs to account for the challenges imposed by the nature of the data. We propose likelihood ratio based cumulative sum (CUSUM) control charts for censored lifetime data with non-normal distributions. We illustrate the development and implementation of the charts, and we evaluate their properties through simulation studies. We address the problem of interval censoring, and we construct a CUSUM chart for censored ordered categorical data, which we illustrate by a case study at Becton Dickinson (BD). We also address the problem of monitoring both of the parameters of the Weibull distribution for processes with right-censored data.
Ph. D.
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Zong, Yujie. "A Sensitivity Analysis of a Nonignorable Nonresponse Model Via EM Algorithm and Bootstrap." Digital WPI, 2011. https://digitalcommons.wpi.edu/etd-theses/208.

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The Slovenian Public Opinion survey (SPOS), which carried out in 1990, was used by the government of Slovenia as a benchmark to prepare for an upcoming plebiscite, which asked the respondents whether they support independence from Yugoslavia. However, the sample size was large and it is quite likely that the respondents and nonrespondents had divergent viewpoints. We first develop an ignorable nonresponse model which is an extension of a bivariate binomial model. In order to accommodate the nonrespondents, we then develop a nonignorable nonresponse model which is an extension of the ignorable model. Our methodology uses an EM algorithm to fit both the ignorable and nonignorable nonresponse models, and estimation is carried out using the bootstrap mechanism. We also perform sensitivity analysis to study different degrees of departures of the nonignorable nonresponse model from the ignorable nonresponse model. We found that the nonignorable nonresponse model is mildly sensitive to departures from the ignorable nonresponse model. In fact, our finding based on the nonignorable model is better than an earlier conclusion about another nonignorable nonresponse model fitted to these data.
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Van, Dyk Hendrik Oostewald. "Classification in high dimensional feature spaces / by H.O. van Dyk." Thesis, North-West University, 2009. http://hdl.handle.net/10394/4091.

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In this dissertation we developed theoretical models to analyse Gaussian and multinomial distributions. The analysis is focused on classification in high dimensional feature spaces and provides a basis for dealing with issues such as data sparsity and feature selection (for Gaussian and multinomial distributions, two frequently used models for high dimensional applications). A Naïve Bayesian philosophy is followed to deal with issues associated with the curse of dimensionality. The core treatment on Gaussian and multinomial models consists of finding analytical expressions for classification error performances. Exact analytical expressions were found for calculating error rates of binary class systems with Gaussian features of arbitrary dimensionality and using any type of quadratic decision boundary (except for degenerate paraboloidal boundaries). Similarly, computationally inexpensive (and approximate) analytical error rate expressions were derived for classifiers with multinomial models. Additional issues with regards to the curse of dimensionality that are specific to multinomial models (feature sparsity) were dealt with and tested on a text-based language identification problem for all eleven official languages of South Africa.
Thesis (M.Ing. (Computer Engineering))--North-West University, Potchefstroom Campus, 2009.
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Florence, Lindsay Walker. "Skill Evaluation in Women's Volleyball." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2286.pdf.

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Allan, Michelle L. "Measuring Skill Importance in Women's Soccer and Volleyball." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd2809.pdf.

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Huynh, Huy. "Estimating the maximum probability of categorical classes with applications to biological diversity measurements." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44868.

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The study of biological diversity has seen a tremendous growth over the past few decades. Among the commonly used indices capturing both the richness and evenness of a community, the Berger-Parker index, which relates to the maximum proportion of all species, is particularly effective. However, when the number of individuals and species grows without bound this index changes, and it is important to develop statistical tools to measure this change. In this thesis, we introduce two estimators for this maximum: the multinomial maximum and the length of the longest increasing subsequence. In both cases, the limiting distribution of the estimators, as the number of individuals and species simultaneously grows without bound, is obtained. Then, constructing the 95% confidence intervals for the maximum proportion helps improve the comparison of the Berger-Parker index among communities. Finally, we compare the two approaches by examining their associated bias corrected estimators and apply our results to environmental data.
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Xue, Huitian, and 薛惠天. "Maximum likelihood estimation of parameters with constraints in normaland multinomial distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B47850012.

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Motivated by problems in medicine, biology, engineering and economics, con- strained parameter problems arise in a wide variety of applications. Among them the application to the dose-response of a certain drug in development has attracted much interest. To investigate such a relationship, we often need to conduct a dose- response experiment with multiple groups associated with multiple dose levels of the drug. The dose-response relationship can be modeled by a shape-restricted normal regression. We develop an iterative two-step ascent algorithm to estimate normal means and variances subject to simultaneous constraints. Each iteration consists of two parts: an expectation{maximization (EM) algorithm that is utilized in Step 1 to compute the maximum likelihood estimates (MLEs) of the restricted means when variances are given, and a newly developed restricted De Pierro algorithm that is used in Step 2 to find the MLEs of the restricted variances when means are given. These constraints include the simple order, tree order, umbrella order, and so on. A bootstrap approach is provided to calculate standard errors of the restricted MLEs. Applications to the analysis of two real datasets on radioim-munological assay of cortisol and bioassay of peptides are presented to illustrate the proposed methods. Liu (2000) discussed the maximum likelihood estimation and Bayesian estimation in a multinomial model with simplex constraints by formulating this constrained parameter problem into an unconstrained parameter problem in the framework of missing data. To utilize the EM and data augmentation (DA) algorithms, he introduced latent variables {Zil;Yil} (to be defined later). However, the proposed DA algorithm in his paper did not provide the necessary individual conditional distributions of Yil given (the observed data and) the updated parameter estimates. Indeed, the EM algorithm developed in his paper is based on the assumption that{ Yil} are fixed given values. Fortunately, the EM algorithm is invariant under any choice of the value of Yil, so the final result is always correct. We have derived the aforesaid conditional distributions and hence provide a valid DA algorithm. A real data set is used for illustration.
published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy
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Petrie, John Eric. "The Accuracy of River Bed Sediment Samples." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/30957.

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One of the most important factors that influences a stream's hydraulic and ecological health is the streambed's sediment size distribution. This distribution affects streambed stability, sediment transport rates, and flood levels by defining the roughness of the stream channel. Adverse effects on water quality and wildlife can be expected when excessive fine sediments enter a stream. Many chemicals and toxic materials are transported through streams by binding to fine sediments. Increases in fine sediments also seriously impact the survival of fish species present in the stream. Fine sediments fill tiny spaces between larger particles thereby denying fish embryos the necessary fresh water to survive. Reforestation, constructed wetlands, and slope stabilization are a few management practices typically utilized to reduce the amount of sediment entering a stream. To effectively gauge the success of these techniques, the sediment size distribution of the stream must be monitored. Gravel bed streams are typically stratified vertically, in terms of particle size, in three layers, with each layer having its own distinct grain size distribution. The top two layers of the stream bed, the pavement and subpavement, are the most significant in determining the characteristics of the stream. These top two layers are only as thick as the largest particle size contained within each layer. This vertical stratification by particle size makes it difficult to characterize the grain size distribution of the surface layer. The traditional bulk or volume sampling procedure removes a specified volume of material from the stream bed. However, if the bed exhibits vertical stratification, the volume sample will mix different populations, resulting in inaccurate sample results. To obtain accurate results for the pavement size distribution, a surface oriented sampling technique must be employed. The most common types of surface oriented sampling are grid and areal sampling. Due to limitations in the sampling techniques, grid samples typically truncate the sample at the finer grain sizes, while areal samples typically truncate the sample at the coarser grain sizes. When combined with an analysis technique, either frequency-by-number or frequency-by-weight, the sample results can be represented in terms of a cumulative grain size distribution. However, the results of different sampling and analysis procedures can lead to biased results, which are not equivalent to traditional volume sampling results. Different conversions, dependent on both the sampling and analysis technique, are employed to remove the bias from surface sample results. The topic of the present study is to determine the accuracy of sediment samples obtained by the different sampling techniques. Knowing the accuracy of a sample is imperative if the sample results are to be meaningful. Different methods are discussed for placing confidence intervals on grid sample results based on statistical distributions. The binomial distribution and its approximation with the normal distribution have been suggested for these confidence intervals in previous studies. In this study, the use of the multinomial distribution for these confidence intervals is also explored. The multinomial distribution seems to best represent the grid sampling process. Based on analyses of the different distributions, recommendations are made. Additionally, figures are given to estimate the grid sample size necessary to achieve a required accuracy for each distribution. This type of sample size determination figure is extremely useful when preparing for grid sampling in the field. Accuracy and sample size determination for areal and volume samples present difficulties not encountered with grid sampling. The variability in number of particles contained in the sample coupled with the wide range of particle sizes present make direct statistical analysis impossible. Limited studies have been reported on the necessary volume to sample for gravel deposits. The majority of these studies make recommendations based on empirical results that may not be applicable to different size distributions. Even fewer studies have been published that address the issue of areal sample size. However, using grid sample results as a basis, a technique is presented to estimate the necessary sizes for areal and volume samples. These areal and volume sample sizes are designed to match the accuracy of the original grid sample for a specified grain size percentile of interest. Obtaining grid and areal results with the same accuracy can be useful when considering hybrid samples. A hybrid sample represents a combination of grid and areal sample results that give a final grain size distribution curve that is not truncated. Laboratory experiments were performed on synthetic stream beds to test these theories. The synthetic stream beds were created using both glass beads and natural sediments. Reducing sampling errors and obtaining accurate samples in the field are also briefly discussed. Additionally, recommendations are also made for using the most efficient sampling technique to achieve the required accuracy.
Master of Science
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Meister, Kadri. "On Methods for Real Time Sampling and Distributions in Sampling." Doctoral thesis, Umeå : Univ, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-415.

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Books on the topic "Multinomial distribution"

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Cheng, Russell. Box-Cox Transformations. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0010.

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This chapter examines the well-known Box-Cox method, which transforms a sample of non-normal observations into approximately normal form. Two non-standard aspects are highlighted. First, the likelihood of the transformed sample has an unbounded maximum, so that the maximum likelihood estimate is not consistent. The usually suggested remedy is to assume grouped data so that the sample becomes multinomial. An alternative method is described that uses a modified likelihood similar to the spacings function. This eliminates the infinite likelihood problem. The second problem is that the power transform used in the Box-Cox method is left-bounded so that the transformed observations cannot be exactly normal. This biases estimates of observational probabilities in an uncertain way. Moreover, the distributions fitted to the observations are not necessarily unimodal. A simple remedy is to assume the transformed observations have a left-bounded distribution, like the exponential; this is discussed in detail, and a numerical example given.
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Thurner, Stefan, Rudolf Hanel, and Peter Klimekl. Statistical Mechanics and Information Theory for Complex Systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821939.003.0006.

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Most complex systems are statistical systems. Statsitical mechanics and information theory usually do not apply to complex systems because the latter break the assumptions of ergodicity, independence, and multinomial statistics. We show that it is possible to generalize the frameworks of statistical mechanics and information theory in a meaningful way, such that they become useful for understanding the statistics of complex systems.We clarify that the notion of entropy for complex systems is strongly dependent on the context where it is used, and differs if it is used as an extensive quantity, a measure of information, or as a tool for statistical inference. We show this explicitly for simple path-dependent complex processes such as Polya urn processes, and sample space reducing processes.We also show it is possible to generalize the maximum entropy principle to path-dependent processes and how this can be used to compute timedependent distribution functions of history dependent processes.
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Book chapters on the topic "Multinomial distribution"

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Seber, George A. F. "Multinomial Distribution." In International Encyclopedia of Statistical Science, 882–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_388.

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Seber, George A. F. "Multinomial Distribution." In Springer Series in Statistics, 181–88. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21930-1_12.

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Andersen, Erling B., Niels-Erik Jensen, and Nils Kousgaard. "Applications of the Multinomial Distribution." In Statistics for Economics, Business Administration, and the Social Sciences, 386–402. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-95528-0_18.

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Jordanova, Pavlina, Monika P. Petkova, and Milan Stehlík. "Compound Log-Series Distribution with Negative Multinomial Summands." In Lecture Notes in Computer Science, 383–90. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57099-0_42.

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Adams, Raymond J., and Margaret L. Wu. "The Mixed-Coefficients Multinomial Logit Model: A Generalized Form of the Rasch Model." In Multivariate and Mixture Distribution Rasch Models, 57–75. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-49839-3_4.

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Hasnat, Md Abul, Julien Velcin, Stéphane Bonnevay, and Julien Jacques. "Simultaneous Clustering and Model Selection for Multinomial Distribution: A Comparative Study." In Advances in Intelligent Data Analysis XIV, 120–31. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24465-5_11.

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Fagerland, Morten W., Stian Lydersen, and Petter Laake. "The 1 × c $ 1\times c $ Table and the Multinomial Distribution." In Statistical Analysis of Contingency Tables, 67–84. Boca Raton, Florida : CRC Press, [2017]: Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315374116-3.

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Yamagishi, Yuki, and Kazumi Saito. "Visualizing Switching Regimes Based on Multinomial Distribution in Buzz Marketing Sites." In Lecture Notes in Computer Science, 385–95. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60438-1_38.

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Trenkler, Götz. "On a Generalisation of the Covariance Matrix of the Multinomial Distribution." In Innovations in Multivariate Statistical Analysis, 67–73. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4615-4603-0_4.

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Epitropakis, Michael G., Dimirtis K. Tasoulis, Nicos G. Pavlidis, Vassilis P. Plagianakos, and Michael N. Vrahatis. "Tracking Differential Evolution Algorithms: An Adaptive Approach through Multinomial Distribution Tracking with Exponential Forgetting." In Lecture Notes in Computer Science, 214–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30448-4_27.

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Conference papers on the topic "Multinomial distribution"

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Kaji, Yuichi. "Bounds on the entropy of multinomial distribution." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282678.

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Turowski, Krzysztof, Philippe Jacquet, and Wojciech Szpankowski. "Asymptotics of Entropy of the Dirichlet-Multinomial Distribution." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849466.

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Zheng, Xiawu, Rongrong Ji, Lang Tang, Baochang Zhang, Jianzhuang Liu, and Qi Tian. "Multinomial Distribution Learning for Effective Neural Architecture Search." In 2019 IEEE/CVF International Conference on Computer Vision (ICCV). IEEE, 2019. http://dx.doi.org/10.1109/iccv.2019.00139.

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Jordanova, Pavlina K., Monika P. Petkova, and Milan Stehlík. "Compound negative binomial distribution with negative multinomial summands." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’16): Proceedings of the 42nd International Conference on Applications of Mathematics in Engineering and Economics. Author(s), 2016. http://dx.doi.org/10.1063/1.4968501.

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Xu, Zuobing, and Ram Akella. "A new probabilistic retrieval model based on the dirichlet compound multinomial distribution." In the 31st annual international ACM SIGIR conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1390334.1390408.

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Kuropatwinski, Marcin. "Estimation of Quantities Related to the Multinomial Distribution with Unknown Number of Categories." In 2019 Signal Processing Symposium (SPSympo). IEEE, 2019. http://dx.doi.org/10.1109/sps.2019.8881992.

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Lertmaneekarn, Bancha, Natthapol Moolsiri, Thanyawarat Pawasopon, and Suvepon Sittichivapak. "Performance analysis of multinomial distribution of group assignment framed ALOHA for multiple RFID." In 2014 11th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON). IEEE, 2014. http://dx.doi.org/10.1109/ecticon.2014.6839857.

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Elkan, Charles. "Clustering documents with an exponential-family approximation of the Dirichlet compound multinomial distribution." In the 23rd international conference. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1143844.1143881.

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Epitropakis, M. G., D. K. Tasoulis, N. G. Pavlidis, V. P. Plagianakos, and M. N. Vrahatis. "Tracking Particle Swarm Optimizers: An adaptive approach through multinomial distribution tracking with exponential forgetting." In 2012 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2012. http://dx.doi.org/10.1109/cec.2012.6256425.

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Daghyani, Masoud, Nuha Zamzami, and Nizar Bouguila. "Efficient Computation of Log-likelihood Function in Clustering Overdispersed Count Data Using Multinomial Beta-Liouville Distribution." In 2019 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE, 2019. http://dx.doi.org/10.1109/ssci44817.2019.9003076.

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Reports on the topic "Multinomial distribution"

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Fox, Jeremy. A Note on Nonparametric Identification of Distributions of Random Coefficients in Multinomial Choice Models. Cambridge, MA: National Bureau of Economic Research, July 2017. http://dx.doi.org/10.3386/w23621.

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