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Journal articles on the topic 'Multinomial distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Gall, Françoise Le. "The modes of a negative multinomial distribution." Statistics & Probability Letters 76, no. 6 (March 2006): 619–24. http://dx.doi.org/10.1016/j.spl.2005.09.009.

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12

Choi, Sung C., and Susan E. Hodge. "Sequential tests for an ordered multinomial distribution." Sequential Analysis 5, no. 1 (January 1986): 73–83. http://dx.doi.org/10.1080/07474948608836091.

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13

Burks, Robert E. "Jelly belly mixing and uniform multinomial distribution." CHANCE 24, no. 1 (March 2011): 24–28. http://dx.doi.org/10.1007/s00144-011-0006-9.

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14

Jokiel-Rokita, Alicja. "Gamma-Minimax Prediction for the Multinomial Distribution." Metrika 64, no. 3 (April 8, 2006): 259–69. http://dx.doi.org/10.1007/s00184-006-0047-x.

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15

Li, Kang, Xian-ming Shi, Juan Li, Mei Zhao, and Chunhua Zeng. "Bayesian Estimation of Ammunition Demand Based on Multinomial Distribution." Discrete Dynamics in Nature and Society 2021 (April 29, 2021): 1–11. http://dx.doi.org/10.1155/2021/5575335.

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In view of the small sample size of combat ammunition trial data and the difficulty of forecasting the demand for combat ammunition, a Bayesian inference method based on multinomial distribution is proposed. Firstly, considering the different damage grades of ammunition hitting targets, the damage results are approximated as multinomial distribution, and a Bayesian inference model of ammunition demand based on multinomial distribution is established, which provides a theoretical basis for forecasting the ammunition demand of multigrade damage under the condition of small samples. Secondly, the conjugate Dirichlet distribution of multinomial distribution is selected as a prior distribution, and Dempster–Shafer evidence theory (D-S theory) is introduced to fuse multisource previous information. Bayesian inference is made through the Markov chain Monte Carlo method based on Gibbs sampling, and ammunition demand at different damage grades is obtained by referring to cumulative damage probability. The study result shows that the Bayesian inference method based on multinomial distribution is highly maneuverable and can be used to predict ammunition demand of different damage grades under the condition of small samples.

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16

Beaulieu, N. C. "On the generalized multinomial distribution, optimal multinomial detectors, and generalized weighted partial decision detectors." IEEE Transactions on Communications 39, no. 2 (1991): 193–94. http://dx.doi.org/10.1109/26.76452.

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17

Afendras, Giorgos, and Vassilis Papathanasiou. "A note on a variance bound for the multinomial and the negative multinomial distribution." Naval Research Logistics (NRL) 61, no. 3 (February 19, 2014): 179–83. http://dx.doi.org/10.1002/nav.21575.

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18

Waller, Lance A., and Daniel Zelterman. "Log-Linear Modeling with the Negative Multinomial Distribution." Biometrics 53, no. 3 (September 1997): 971. http://dx.doi.org/10.2307/2533557.

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19

Jammalamadaka, S. Rao, and Sudeep R. Bapat. "Middle censoring in the multinomial distribution with applications." Statistics & Probability Letters 167 (December 2020): 108916. http://dx.doi.org/10.1016/j.spl.2020.108916.

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20

Chang, Guisong, and Tianming Wang. "Genome analysis with the conditional multinomial distribution profile." Journal of Theoretical Biology 271, no. 1 (February 2011): 44–50. http://dx.doi.org/10.1016/j.jtbi.2010.11.034.

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21

Gall, Françoise Le. "Determination of the modes of a Multinomial distribution." Statistics & Probability Letters 62, no. 4 (May 2003): 325–33. http://dx.doi.org/10.1016/s0167-7152(02)00430-3.

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22

Trybuła, Stanisław. "Simultaneous minimax estimation of parameters of multinomial distribution." Applicationes Mathematicae 29, no. 3 (2002): 307–11. http://dx.doi.org/10.4064/am29-3-4.

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23

Paul, Sudhir R., Uditha Balasooriya, and Tathagata Banerjee. "Fisher Information Matrix of the Dirichlet-multinomial Distribution." Biometrical Journal 47, no. 2 (April 2005): 230–36. http://dx.doi.org/10.1002/bimj.200410103.

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24

Jokiel-Rokita, Alicja, and Ryszard Magiera. "Estimation with Delayed Bservations for the Multinomial Distribution." Statistics 32, no. 4 (January 1999): 353–67. http://dx.doi.org/10.1080/02331889908802675.

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25

Diamond, Charles A., Curtis J. Simon, and John T. Warner. "A multinomial probability model of size income distribution." Journal of Econometrics 43, no. 1-2 (January 1990): 43–61. http://dx.doi.org/10.1016/0304-4076(90)90106-4.

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26

Puente, Carlos E. "Multinomial multifractals, fractal interpolators, and the Gaussian distribution." Physics Letters A 161, no. 5 (January 1992): 441–47. http://dx.doi.org/10.1016/0375-9601(92)90685-f.

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27

Diaconis, Persi, and Robert C. Griffiths. "Reproducing kernel orthogonal polynomials on the multinomial distribution." Journal of Approximation Theory 242 (June 2019): 1–30. http://dx.doi.org/10.1016/j.jat.2019.01.007.

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28

Roos, Bero, and Bero Roos. "Metric multivariate Poisson approximation of the generalized multinomial distribution." Teoriya Veroyatnostei i ee Primeneniya 43, no. 2 (1998): 404–13. http://dx.doi.org/10.4213/tvp1480.

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29

Geelhoed, B., and H. J. Glass. "Estimators for particulate sampling derived from a multinomial distribution." Statistica Neerlandica 58, no. 1 (February 2004): 57–74. http://dx.doi.org/10.1046/j.0039-0402.2003.00106.x.

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30

Neudecker, H. "Mathematical Properties of the Variance of the Multinomial Distribution." Journal of Mathematical Analysis and Applications 189, no. 3 (February 1995): 757–62. http://dx.doi.org/10.1006/jmaa.1995.1049.

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31

Chuang, Christy, and Christopher Cox. "Pseudo maximum likelihood estimation for the dirichlet-multinomial distribution." Communications in Statistics - Theory and Methods 14, no. 10 (January 1985): 2293–311. http://dx.doi.org/10.1080/03610928508829045.

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32

Bhandari, Subir Kumar, and Arup Bose. "Selecting the t-best cells in a multinomial distribution." Communications in Statistics - Theory and Methods 18, no. 9 (January 1989): 3313–26. http://dx.doi.org/10.1080/03610928908830094.

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33

Roos, B. "Metric Multivariate Poisson Approximation of the Generalized Multinomial Distribution." Theory of Probability & Its Applications 43, no. 2 (January 1999): 306–16. http://dx.doi.org/10.1137/s0040585x97976921.

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34

MOREL, JORGE G., and NEERCHAL K. NAGARAJ. "A finite mixture distribution for modelling multinomial extra variation." Biometrika 80, no. 2 (1993): 363–71. http://dx.doi.org/10.1093/biomet/80.2.363.

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35

Ogura, Hiroshi, Hiromi Amano, and Masato Kondo. "Gamma-Poisson Distribution Model for Text Categorization." ISRN Artificial Intelligence 2013 (April 4, 2013): 1–17. http://dx.doi.org/10.1155/2013/829630.

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We introduce a new model for describing word frequency distributions in documents for automatic text classification tasks. In the model, the gamma-Poisson probability distribution is used to achieve better text modeling. The framework of the modeling and its application to text categorization are demonstrated with practical techniques for parameter estimation and vector normalization. To investigate the efficiency of our model, text categorization experiments were performed on 20 Newsgroups, Reuters-21578, Industry Sector, and TechTC-100 datasets. The results show that the model allows performance comparable to that of the support vector machine and clearly exceeding that of the multinomial model and the Dirichlet-multinomial model. The time complexity of the proposed classifier and its advantage in practical applications are also discussed.

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36

Chen, Youhua, Yongbin Wu, Weihua Chen, Tian Zhao, Wenyan Zhang, and Tsung-Jen Shen. "Application of a Negative Multinomial Model Gives Insight into Rarity-Area Relationships." Forests 11, no. 5 (May 20, 2020): 571. http://dx.doi.org/10.3390/f11050571.

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The distribution of individuals of different species across different sampling units is typically non-random. This distributional non-independence can be interpreted and modelled as a correlated multivariate distribution. However, this correlation cannot be modelled using a totally independent and random distribution such as the Poisson distribution. In this study, we utilized the negative multinomial distribution to overcome the problem encountered by the commonly used Poisson distribution and used it to derive insight into the implications of field sampling for rare species’ distributions. Mathematically, we derived, from the negative multinomial distribution and sampling theory, contrasting relationships between sampling area, and the proportions of locally rare and regionally rare species in ecological assemblages presenting multi-species correlated distribution. With the suggested model, we explored the cross-scale relationships between the spatial extent, the population threshold for defining the rarity of species, and the multi-species correlated distribution pattern using data from two 50-ha tropical forest plots in Barro Colorado Island (Panama) and Heishiding Provincial Reserve (Guangdong Province, China). Notably, unseen species (species with zero abundance in the studied local sample) positively contributed to the distributional non-independence of species in a local sample. We empirically confirmed these findings using the plot data. These findings can help predict rare species–area relationships at various spatial scales, potentially informing biodiversity conservation and development of optimal field sampling strategies.

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37

Muliere, Pietro, and Piercesare Secchi. "Weak Convergence of a Dirichlet-Multinomial Process." gmj 10, no. 2 (June 2003): 319–24. http://dx.doi.org/10.1515/gmj.2003.319.

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Abstract We present a random probability distribution which approximates, in the sense of weak convergence, the Dirichlet process and supports a Bayesian resampling plan called a proper Bayesian bootstrap.

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38

Mirakhmedov, Sh A. "Approximation of the Distribution of Multidimensional Randomized Divisible Statistics by Normal Distributions (Multinomial Scheme)." Theory of Probability & Its Applications 32, no. 4 (December 1988): 696–706. http://dx.doi.org/10.1137/1132102.

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39

Guimarães, Paulo. "A Simple Approach to Fit the Beta-binomial Model." Stata Journal: Promoting communications on statistics and Stata 5, no. 3 (September 2005): 385–94. http://dx.doi.org/10.1177/1536867x0500500307.

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In this paper, I show how to estimate the parameters of the beta-binomial distribution and its multivariate generalization, the Dirichlet-multinomial distribution. This approach involves no additional programming, as it relies on an existing Stata command used for overdispersed count panel data. Including covariates to allow for regression models based in these distributions is straightforward.

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40

Hrafnkelsson, Birgir, and Gunnar Stefánsson. "A model for categorical length data from groundfish surveys." Canadian Journal of Fisheries and Aquatic Sciences 61, no. 7 (July 1, 2004): 1135–42. http://dx.doi.org/10.1139/f04-049.

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An extension of the multinomial model of counts is presented to account for overdispersion and different correlation structure. Such models are needed in biological applications such as the analysis of length measurements from surveys of heterogeneous populations used for assessments of marine resources. One of the goals of such a survey is to estimate the length distribution of each species within a particular area. Using data on Atlantic cod (Gadus morhua) in Icelandic waters, it is demonstrated that the assumptions used in practice for categorical length data are seriously violated. The length data on cod exhibit variances that are larger than those of the standard multinomial model and correlation coefficients that are greater than those of the Dirichlet-multinomial model. To alleviate these problems, a hierarchical model based on the multinomial distribution and the logistically transformed multivariate Gaussian distribution is proposed. It is illustrated that this model captures the complex covariance structure of the data. The parameters in the models are estimated using a Bayesian estimation procedure based on Markov chain Monte Carlo.

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41

Anisi, Mohammad, and Morteza Analoui. "Multinomial Agent's Trust Modeling Using Entropy of the Dirichlet Distribution." International Journal of Artificial Intelligence & Applications 2, no. 3 (July 31, 2011): 1–11. http://dx.doi.org/10.5121/ijaia.2011.2301.

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42

Rukhin, Andrew L. "Gamma-distribution order statistics, maximal multinomial frequency and randomization designs." Journal of Statistical Planning and Inference 136, no. 7 (July 2006): 2213–26. http://dx.doi.org/10.1016/j.jspi.2005.08.027.

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43

Bénasséni, Jacques. "A new derivation of eigenvalue inequalities for the multinomial distribution." Journal of Mathematical Analysis and Applications 393, no. 2 (September 2012): 697–98. http://dx.doi.org/10.1016/j.jmaa.2012.03.029.

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44

Neveu, D., A. Kramar, and P. Dujols. "Corrected asymptotic distribution of statistics based on the multinomial law." Statistical Methodology 4, no. 1 (January 2007): 64–74. http://dx.doi.org/10.1016/j.stamet.2006.06.003.

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45

Chen, LanXiang, J. Eichenauer-Herrmann, and J. Lehn. "Gamma-minimax estimators for the parameters of a multinomial distribution." Applicationes Mathematicae 20, no. 4 (1988): 561–64. http://dx.doi.org/10.4064/am-20-4-561-564.

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46

Jokiel-Rokita, Alicja, and Ryszard Magiera. "Γ-minimax estimation with delayed observations from the multinomial distribution." Statistics 38, no. 3 (June 2004): 195–206. http://dx.doi.org/10.1080/02331880410001696099.

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47

Trybula, Stanislaw. "Systematic estimation of parameters of multinomial and multivariate hypergeometric distribution." Statistics 22, no. 1 (January 1991): 59–67. http://dx.doi.org/10.1080/02331889108802284.

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48

Lee, Chu-In Charles, Wei Liu, Chul Gyu Park, and Jianan Peng. "Inference for comparing a multinomial distribution with a known standard." Statistical Papers 53, no. 3 (April 19, 2011): 775–88. http://dx.doi.org/10.1007/s00362-011-0380-7.

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49

Dasgupta, Ratan, and Sisir Roy. "Multinomial Distribution, Quantum Statistics and Einstein-Podolsky-Rosen Like Phenomena." Foundations of Physics 38, no. 4 (January 23, 2008): 384–94. http://dx.doi.org/10.1007/s10701-008-9207-3.

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50

Malefaki, Sonia, and George Iliopoulos. "Simulating from a multinomial distribution with large number of categories." Computational Statistics & Data Analysis 51, no. 12 (August 2007): 5471–76. http://dx.doi.org/10.1016/j.csda.2007.03.022.

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