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Books on the topic 'Mixture of lognormal distributions'

Author: Grafiati

Published: 18 April 2022

Last updated: 30 July 2025

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1

L, Crow Edwin, and Shimizu Kunio 1948-, eds. Lognormal distributions: Theory and applications. M. Dekker, 1988.

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2

Lachos Dávila, Víctor Hugo, Celso Rômulo Barbosa Cabral, and Camila Borelli Zeller. Finite Mixture of Skewed Distributions. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98029-4.

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3

Titterington, D. M. Statistical analysis of finite mixture distributions. Wiley, 1985.

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4

Balakrishnan, N., and William W. S. Chen. Handbook of Tables for Order Statistics from Lognormal Distributions with Applications. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5309-0.

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5

S, Chen William W., ed. Handbook of tables for order statistics from lognormal distributions with applications. Kluwer Academic Publishers, 1999.

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6

R, Hancock Gregory, and Samuelsen Karen M, eds. Advances in latent variable mixture models. Information Age Pub., 2008.

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7

Evans, Michael J. Numerical aspects in estimating the parameters of a mixture of normal distributions. University of Toronto, Dept. of Statistics, 1991.

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8

Ćwik, Jan. Nonidentifiability of components in a mixture of distributions corresponding to repeated observations. Institute of Computer Sciences, Polish Academy of Sciences, 1991.

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9

Gellert, Charles Lawrence. Misaligned (shuffled) data analysis with application to gene regulation. University at Albany, School of Public Health, Dept. of Biometry and Statistics, 1990.

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10

service), SpringerLink (Online, ed. Medical Applications of Finite Mixture Models. Springer-Verlag Berlin Heidelberg, 2009.

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11

Cheng, Russell. Finite Mixture Examples; MAPIS Details. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0018.

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Two detailed numerical examples are given in this chapter illustrating and comparing mainly the reversible jump Markov chain Monte Carlo (RJMCMC) and the maximum a posteriori/importance sampling (MAPIS) methods. The numerical examples are the well-known galaxy data set with sample size 82, and the Hidalgo stamp issues thickness data with sample size 485. A comparison is made of the estimates obtained by the RJMCMC and MAPIS methods for (i) the posterior k-distribution of the number of components, k, (ii) the predictive finite mixture distribution itself, and (iii) the posterior distributions o

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12

Crow. Lognormal Distributions: Theory and Applications. CRC Press LLC, 2018.

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13

Crow. Lognormal Distributions: Theory and Applications. CRC Press LLC, 2018.

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14

Crow. Lognormal Distributions: Theory and Applications. CRC Press LLC, 2018.

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15

Crow. Lognormal Distributions: Theory and Applications. CRC Press LLC, 2018.

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16

Crow. Lognormal Distributions: Theory and Applications. CRC Press LLC, 2020.

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17

Finite Mixture Distributions. Springer, 2011.

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18

Everitt, B. Finite Mixture Distributions. Springer, 2013.

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19

Dávila, Víctor Hugo Lachos, Celso Rômulo Barbosa Cabral, and Camila Borelli Zeller. Finite Mixture of Skewed Distributions. Springer, 2018.

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20

Peel, David, and Geoffrey J. McLachlan. Finite Mixture Models. Wiley & Sons, Incorporated, John, 2005.

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21

Peel, David, and Geoffrey J. McLachlan. Finite Mixture Models. Wiley & Sons, Incorporated, John, 2007.

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22

Peel, David, and Geoffrey J. McLachlan. Finite Mixture Models. Wiley & Sons, Incorporated, John, 2004.

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23

Crow. Lognormal Distributions (Statistics: a Series of Textbooks and Monogrphs). CRC, 1987.

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24

Balakrishnan, N., and W. S. Chen. Handbook of Tables for Order Statistics from Lognormal Distributions with Applications. Springer London, Limited, 2013.

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25

Handbook of Tables for Order Statistics from Lognormal Distributions with Applications. Springer, 1999.

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26

Robert, Christian, Kerrie L. Mengersen, and Mike Titterington. Mixtures: Estimation and Applications. Wiley & Sons, Incorporated, John, 2011.

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27

Hancock, Gregory R., and Karen M. Samuelsen. Advances in Latent Variable Mixture Models. Information Age Publishing, Incorporated, 2007.

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28

Celeux, Gilles, Christian P. Robert, and Sylvia Fruhwirth-Schnatter. Handbook of Mixture Analysis. Taylor & Francis Group, 2019.

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29

Celeux, Gilles, Christian P. Robert, and Sylvia Fruhwirth-Schnatter. Handbook of Mixture Analysis. Taylor & Francis Group, 2019.

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30

Celeux, Gilles, Christian P. Robert, and Sylvia Fruhwirth-Schnatter. Handbook of Mixture Analysis. Taylor & Francis Group, 2019.

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31

Frühwirth-Schnatter, Sylvia, Gilles Celeux, and Christian P. Robert. Handbook of Mixture Analysis. Taylor & Francis Group, 2020.

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32

Handbook of Mixture Analysis. Taylor & Francis Group, 2019.

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33

Cheng, Russell. Examples of Embedded Distributions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0006.

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This chapter gives examples of probability distributions that, in their conventional parametrization, contain embedded models. Embeddedness is not intrinsic but depends on the parametrization. The simplest way to reveal and remove embeddedness is to reparametrize and make the log-likelihood, L, expandable as a Maclaurin series of one parameter, α‎: L = L0 + L1α‎ + L2α‎2 + … with L0 the log-likelihood of the embedded model hidden in the original parametrization. The quantity L1, rescaled using the information matrix, is the score statistic which can be used for formally comparing the original a

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34

Robert, Christian, Kerrie L. Mengersen, and Mike Titterington. Mixtures: Estimation and Applications. Wiley, 2011.

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35

Robert, Christian, Kerrie L. Mengersen, and Mike Titterington. Mixtures: Estimation and Applications. Wiley & Sons, Incorporated, John, 2011.

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36

Robert, Christian, Kerrie L. Mengersen, and Mike Titterington. Mixtures: Estimation and Applications. Wiley & Sons, Limited, John, 2011.

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37

Robert, Christian, Kerrie Mengersen, and Mike Titterington. Mixtures. Wiley & Sons, Incorporated, John, 2012.

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38

Robert, Christian, Kerrie Mengersen, and Mike Titterington. Mixtures: Estimation and Applications. Wiley & Sons, Incorporated, John, 2011.

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39

(Editor), Gregory R. Hancock, and Karen M. Samuelsen (Editor), eds. Advances in Latent Variable Mixture Models (HC). Information Age Publishing, 2007.

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40

Cheng, Russell. Finite Mixture Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0017.

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Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain Monte Carlo (MCMC) methods are reviewed and compared with ML: the reversible jump method and one using an approximating Dirichlet process. Another Bayesian method, to be called MAPIS, is examined that first obtains point estimates for the component parameters by the maximum a posteriori method for different k and then estimates posterior distributions, including that for k, using importance sampli

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41

Frühwirth-Schnatter, Sylvia. Finite Mixture and Markov Switching Models. Springer New York, 2010.

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42

Mixture Model-Based Classification. Taylor & Francis Group, 2016.

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43

McNicholas, Paul D. Mixture Model-Based Classification. Taylor & Francis Group, 2016.

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44

McNicholas, Paul D. Mixture Model-Based Classification. Taylor & Francis Group, 2020.

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45

McNicholas, Paul D. Mixture Model-Based Classification. Taylor & Francis Group, 2016.

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46

McNicholas, Paul D. Mixture Model-Based Classification. Taylor & Francis Group, 2016.

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47

McNicholas, Paul D. Mixture Model-Based Classification. Taylor & Francis Group, 2016.

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48

Louhibi, M. E. H. Degradation failure mode of transistors: The use of lognormal and exponential distributions in the reliability analysis of semiconductor devices. 1985.

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49

Linear approximations in convex metric spaces and the application in the mixture theory of probability theory. World Scientific, 1993.

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50

Draper, Norman R., and George E. P. Box. Response Surfaces, Mixtures, and Ridge Analyses. Wiley & Sons, Incorporated, John, 2007.

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