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Finite mixture models [[electronic resource] /] / Geoffrey McLachlan, David Peel
Finite mixture models [[electronic resource] /] / Geoffrey McLachlan, David Peel
Autore McLachlan Geoffrey J. <1946->
Pubbl/distr/stampa New York, : Wiley, c2000
Descrizione fisica 1 online resource (450 p.)
Disciplina 519
519.2
519.532
Altri autori (Persone) PeelDavid <1971->
Collana Wiley series in probability and statistics. Applied probability and statistics section
Soggetto topico Mixture distributions (Probability theory)
Mathematics
ISBN 1-280-26492-6
9786610264926
0-470-34190-4
0-471-65406-X
0-471-72118-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; Preface; 1 General Introduction; 2 ML Fitting of Mixture Models; 3 Multivariate Normal Mixtures; 4 Bayesian Approach to Mixture Analysis; 5 Mixtures with Nonnormal Components; 6 Assessing the Number of Components in Mixture Models; 7 Multivariate t Mixtures; 8 Mixtures of Factor Analyzers; 9 Fitting Mixture Models to Binned Data; 10 Mixture Models for Failure-Time Data; 11 Mixture Analysis of Directional Data; 12 Variants of the EM Algorithm for Large Databases; 13 Hidden Markov Models; Appendix: Mixture Software; References; Author Index; Subject Index
Record Nr. UNINA-9910143199603321
McLachlan Geoffrey J. <1946->  
New York, : Wiley, c2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Finite mixture models [[electronic resource] /] / Geoffrey McLachlan, David Peel
Finite mixture models [[electronic resource] /] / Geoffrey McLachlan, David Peel
Autore McLachlan Geoffrey J. <1946->
Pubbl/distr/stampa New York, : Wiley, c2000
Descrizione fisica 1 online resource (450 p.)
Disciplina 519
519.2
519.532
Altri autori (Persone) PeelDavid <1971->
Collana Wiley series in probability and statistics. Applied probability and statistics section
Soggetto topico Mixture distributions (Probability theory)
Mathematics
ISBN 1-280-26492-6
9786610264926
0-470-34190-4
0-471-65406-X
0-471-72118-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; Preface; 1 General Introduction; 2 ML Fitting of Mixture Models; 3 Multivariate Normal Mixtures; 4 Bayesian Approach to Mixture Analysis; 5 Mixtures with Nonnormal Components; 6 Assessing the Number of Components in Mixture Models; 7 Multivariate t Mixtures; 8 Mixtures of Factor Analyzers; 9 Fitting Mixture Models to Binned Data; 10 Mixture Models for Failure-Time Data; 11 Mixture Analysis of Directional Data; 12 Variants of the EM Algorithm for Large Databases; 13 Hidden Markov Models; Appendix: Mixture Software; References; Author Index; Subject Index
Record Nr. UNINA-9910830949803321
McLachlan Geoffrey J. <1946->  
New York, : Wiley, c2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Finite mixture models / / Geoffrey McLachlan, David Peel
Finite mixture models / / Geoffrey McLachlan, David Peel
Autore McLachlan Geoffrey J. <1946->
Pubbl/distr/stampa New York, : Wiley, c2000
Descrizione fisica 1 online resource (450 p.)
Disciplina 519.2
Altri autori (Persone) PeelDavid <1971->
Collana Wiley series in probability and statistics. Applied probability and statistics section
Soggetto topico Mixture distributions (Probability theory)
Mathematics
ISBN 1-280-26492-6
9786610264926
0-470-34190-4
0-471-65406-X
0-471-72118-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; Preface; 1 General Introduction; 2 ML Fitting of Mixture Models; 3 Multivariate Normal Mixtures; 4 Bayesian Approach to Mixture Analysis; 5 Mixtures with Nonnormal Components; 6 Assessing the Number of Components in Mixture Models; 7 Multivariate t Mixtures; 8 Mixtures of Factor Analyzers; 9 Fitting Mixture Models to Binned Data; 10 Mixture Models for Failure-Time Data; 11 Mixture Analysis of Directional Data; 12 Variants of the EM Algorithm for Large Databases; 13 Hidden Markov Models; Appendix: Mixture Software; References; Author Index; Subject Index
Record Nr. UNINA-9910877772003321
McLachlan Geoffrey J. <1946->  
New York, : Wiley, c2000
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Finite mixture models / Geoffrey McLachlan, David Peel
Finite mixture models / Geoffrey McLachlan, David Peel
Autore McLachlan, Geoffrey J.
Pubbl/distr/stampa New York : Wiley, c2000
Descrizione fisica xxii, 419 p. : ill. ; 25 cm.
Disciplina 519.2
Altri autori (Persone) Peel, Davidauthor
Collana Wiley series in probability and statistics. Applied probability and statistics section
Soggetto topico Mixture distributions (Probability theory)
ISBN 0471006262
Classificazione AMS 60E99
AMS 62E99
LC QA273.6.M395
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991003678689707536
McLachlan, Geoffrey J.  
New York : Wiley, c2000
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Handbook of Mixture Analysis / / edited by Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert
Handbook of Mixture Analysis / / edited by Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert
Edizione [1st ed.]
Pubbl/distr/stampa Milton, : Chapman and Hall/CRC, 2018
Descrizione fisica 1 online resource (522 pages)
Disciplina 519.24
Altri autori (Persone) Frühwirth-SchnatterSylvia <1959->
CeleuxGilles
RobertChristian P. <1961->
Collana Chapman & Hall/CRC handbooks of modern statistical methods
Soggetto topico Mixture distributions (Probability theory)
Distribution (Probability theory)
ISBN 0-429-50886-7
0-429-50824-7
0-429-05591-9
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; Editors; Contributors; List of Symbols; I: Foundations and Methods; 1: Introduction to Finite Mixtures; 1.1 Introduction and Motivation; 1.1.1 Basic formulation; 1.1.2 Likelihood; 1.1.3 Latent allocation variables; 1.1.4 A little history; 1.2 Generalizations; 1.2.1 Infinite mixtures; 1.2.2 Continuous mixtures; 1.2.3 Finite mixtures with nonparametric components; 1.2.4 Covariates and mixtures of experts; 1.2.5 Hidden Markov models; 1.2.6 Spatial mixtures; 1.3 Some Technical Concerns; 1.3.1 Identifiability
1.3.2 Label switching1.4 Inference; 1.4.1 Frequentist inference, and the role of EM; 1.4.2 Bayesian inference, and the role of MCMC; 1.4.3 Variable number of components; 1.4.4 Modes versus components; 1.4.5 Clustering and classification; 1.5 Concluding Remarks; Bibliography; 2: EM Methods for Finite Mixtures; 2.1 Introduction; 2.2 The EM Algorithm; 2.2.1 Description of EM for finite mixtures; 2.2.2 EM as an alternating-maximization algorithm; 2.3 Convergence and Behavior of EM; 2.4 Cousin Algorithms of EM; 2.4.1 Stochastic versions of the EM algorithm; 2.4.2 The Classification EM algorithm
2.5 Accelerating the EM Algorithm2.6 Initializing the EM Algorithm; 2.6.1 Random initialization; 2.6.2 Hierarchical initialization; 2.6.3 Recursive initialization; 2.7 Avoiding Spurious Local Maximizers; 2.8 Concluding Remarks; Bibliography; 3: An Expansive View of EM Algorithms; 3.1 Introduction; 3.2 The Product-of-Sums Formulation; 3.2.1 Iterative algorithms and the ascent property; 3.2.2 Creating a minorizing surrogate function; 3.3 Likelihood as a Product of Sums; 3.4 Non-standard Examples of EM Algorithms; 3.4.1 Modes of a density; 3.4.2 Gradient maxima; 3.4.3 Two-step EM
3.5 Stopping Rules for EM Algorithms3.6 Concluding Remarks; Bibliography; 4: Bayesian Mixture Models: Theory and Methods; 4.1 Introduction; 4.2 Bayesian Mixtures: From Priors to Posteriors; 4.2.1 Models and representations; 4.2.2 Impact of the prior distribution; 4.2.2.1 Conjugate priors; 4.2.2.2 Improper and non-informative priors; 4.2.2.3 Data-dependent priors; 4.2.2.4 Priors for overfitted mixtures; 4.3 Asymptotic Properties of the Posterior Distribution in the Finite Case; 4.3.1 Posterior concentration around the marginal density; 4.3.2 Recovering the parameters in the well-behaved case
4.3.3 Boundary parameters: overfitted mixtures4.3.4 Asymptotic behaviour of posterior estimates of the number of components; 4.4 Concluding Remarks; Bibliography; 5: Computational Solutions for Bayesian Inference in Mixture Models; 5.1 Introduction; 5.2 Algorithms for Posterior Sampling; 5.2.1 A computational problem? Which computational problem?; 5.2.2 Gibbs sampling; 5.2.3 Metropolis-Hastings schemes; 5.2.4 Reversible jump MCMC; 5.2.5 Sequential Monte Carlo; 5.2.6 Nested sampling; 5.3 Bayesian Inference in the Model-Based Clustering Context; 5.4 Simulation Studies
Record Nr. UNINA-9910838292903321
Milton, : Chapman and Hall/CRC, 2018
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Mixture models : theory, geometry, and applications / / Bruce G. Lindsay
Mixture models : theory, geometry, and applications / / Bruce G. Lindsay
Autore Lindsay Bruce G
Pubbl/distr/stampa Institute of Mathematical Statistics
Soggetto topico Mixture distributions (Probability theory)
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Altri titoli varianti Mixture Models
Record Nr. UNINA-9910482882503321
Lindsay Bruce G  
Institute of Mathematical Statistics
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Mixture models : inference and applications to clustering / Geoffrey J. McLachlan, Kaye E. Basford
Mixture models : inference and applications to clustering / Geoffrey J. McLachlan, Kaye E. Basford
Autore McLachlan, Geoffrey J.
Pubbl/distr/stampa New York, N.Y : Marcel Dekker, c1988
Descrizione fisica xi, 253 p. : ill. ; 24 cm.
Disciplina 519.535
Altri autori (Persone) Basford, Kaye E.
Collana Statistics, textbooks and monographs ; 84
Soggetto topico Cluster analysis
Mixture distributions (Probability theory)
ISBN 0824776917
Classificazione AMS 62H30
QA276.7.M39
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISALENTO-991001148739707536
McLachlan, Geoffrey J.  
New York, N.Y : Marcel Dekker, c1988
Materiale a stampa
Lo trovi qui: Univ. del Salento
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Mixtures [[electronic resource] ] : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington
Mixtures [[electronic resource] ] : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington
Pubbl/distr/stampa Chichester, West Sussex, : Wiley, 2011
Descrizione fisica 1 online resource (331 p.)
Disciplina 519.2/4
519.24
Altri autori (Persone) MengersenKerrie L
RobertChristian P. <1961->
TitteringtonD. M
Collana Wiley series in probability and statistics
Soggetto topico Mixture distributions (Probability theory)
Distribution (Probability theory)
ISBN 1-283-40559-8
9786613405593
1-119-99568-X
1-119-99567-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Mixtures: Estimation and Applications; Contents; Preface; Acknowledgements; List of contributors; 1 The EM algorithm, variational approximations and expectation propagation for mixtures; 1.1 Preamble; 1.2 The EM algorithm; 1.2.1 Introduction to the algorithm; 1.2.2 The E-step and the M-step for the mixing weights; 1.2.3 The M-step for mixtures of univariate Gaussian distributions; 1.2.4 M-step for mixtures of regular exponential family distributions formulated in terms of the natural parameters; 1.2.5 Application to other mixtures; 1.2.6 EM as a double expectation
1.3 Variational approximations1.3.1 Preamble; 1.3.2 Introduction to variational approximations; 1.3.3 Application of variational Bayes to mixture problems; 1.3.4 Application to other mixture problems; 1.3.5 Recursive variational approximations; 1.3.6 Asymptotic results; 1.4 Expectation-propagation; 1.4.1 Introduction; 1.4.2 Overview of the recursive approach to be adopted; 1.4.3 Finite Gaussian mixtures with an unknown mean parameter; 1.4.4 Mixture of two known distributions; 1.4.5 Discussion; Acknowledgements; References; 2 Online expectation maximisation; 2.1 Introduction
2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion; 2.3.1 The batch EM algorithm; 2.3.2 The limiting EM recursion; 2.3.3 Limitations of batch EM for long data records; 2.4 Online expectation maximisation; 2.4.1 The algorithm; 2.4.2 Convergence properties; 2.4.3 Application to finite mixtures; 2.4.4 Use for batch maximum-likelihood estimation; 2.5 Discussion; References; 3 The limiting distribution of the EM test of the order of a finite mixture; 3.1 Introduction; 3.2 The method and theory of the EM test; 3.2.1 The definition of the EM test statistic
3.2.2 The limiting distribution of the EM test statistic3.3 Proofs; 3.4 Discussion; References; 4 Comparing Wald and likelihood regions applied to locally identifiable mixture models; 4.1 Introduction; 4.2 Background on likelihood confidence regions; 4.2.1 Likelihood regions; 4.2.2 Profile likelihood regions; 4.2.3 Alternative methods; 4.3 Background on simulation and visualisation of the likelihood regions; 4.3.1 Modal simulation method; 4.3.2 Illustrative example; 4.4 Comparison between the likelihood regions and the Wald regions; 4.4.1 Volume/volume error of the confidence regions
4.4.2 Differences in univariate intervals via worst case analysis4.4.3 Illustrative example (revisited); 4.5 Application to a finite mixture model; 4.5.1 Nonidentifiabilities and likelihood regions for the mixture parameters; 4.5.2 Mixture likelihood region simulation and visualisation; 4.5.3 Adequacy of using the Wald confidence region; 4.6 Data analysis; 4.7 Discussion; References; 5 Mixture of experts modelling with social science applications; 5.1 Introduction; 5.2 Motivating examples; 5.2.1 Voting blocs; 5.2.2 Social and organisational structure; 5.3 Mixture models
5.4 Mixture of experts models
Record Nr. UNINA-9910130863803321
Chichester, West Sussex, : Wiley, 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Mixtures : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington
Mixtures : estimation and applications / / edited by Kerrie L. Mengersen, Christian P. Robert, D. Michael Titterington
Pubbl/distr/stampa Chichester, West Sussex, : Wiley, 2011
Descrizione fisica 1 online resource (331 p.)
Disciplina 519.2/4
Altri autori (Persone) MengersenKerrie L
RobertChristian P. <1961->
TitteringtonD. M
Collana Wiley series in probability and statistics
Soggetto topico Mixture distributions (Probability theory)
Distribution (Probability theory)
ISBN 1-283-40559-8
9786613405593
1-119-99568-X
1-119-99567-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Mixtures: Estimation and Applications; Contents; Preface; Acknowledgements; List of contributors; 1 The EM algorithm, variational approximations and expectation propagation for mixtures; 1.1 Preamble; 1.2 The EM algorithm; 1.2.1 Introduction to the algorithm; 1.2.2 The E-step and the M-step for the mixing weights; 1.2.3 The M-step for mixtures of univariate Gaussian distributions; 1.2.4 M-step for mixtures of regular exponential family distributions formulated in terms of the natural parameters; 1.2.5 Application to other mixtures; 1.2.6 EM as a double expectation
1.3 Variational approximations1.3.1 Preamble; 1.3.2 Introduction to variational approximations; 1.3.3 Application of variational Bayes to mixture problems; 1.3.4 Application to other mixture problems; 1.3.5 Recursive variational approximations; 1.3.6 Asymptotic results; 1.4 Expectation-propagation; 1.4.1 Introduction; 1.4.2 Overview of the recursive approach to be adopted; 1.4.3 Finite Gaussian mixtures with an unknown mean parameter; 1.4.4 Mixture of two known distributions; 1.4.5 Discussion; Acknowledgements; References; 2 Online expectation maximisation; 2.1 Introduction
2.2 Model and assumptions2.3 The EM algorithm and the limiting EM recursion; 2.3.1 The batch EM algorithm; 2.3.2 The limiting EM recursion; 2.3.3 Limitations of batch EM for long data records; 2.4 Online expectation maximisation; 2.4.1 The algorithm; 2.4.2 Convergence properties; 2.4.3 Application to finite mixtures; 2.4.4 Use for batch maximum-likelihood estimation; 2.5 Discussion; References; 3 The limiting distribution of the EM test of the order of a finite mixture; 3.1 Introduction; 3.2 The method and theory of the EM test; 3.2.1 The definition of the EM test statistic
3.2.2 The limiting distribution of the EM test statistic3.3 Proofs; 3.4 Discussion; References; 4 Comparing Wald and likelihood regions applied to locally identifiable mixture models; 4.1 Introduction; 4.2 Background on likelihood confidence regions; 4.2.1 Likelihood regions; 4.2.2 Profile likelihood regions; 4.2.3 Alternative methods; 4.3 Background on simulation and visualisation of the likelihood regions; 4.3.1 Modal simulation method; 4.3.2 Illustrative example; 4.4 Comparison between the likelihood regions and the Wald regions; 4.4.1 Volume/volume error of the confidence regions
4.4.2 Differences in univariate intervals via worst case analysis4.4.3 Illustrative example (revisited); 4.5 Application to a finite mixture model; 4.5.1 Nonidentifiabilities and likelihood regions for the mixture parameters; 4.5.2 Mixture likelihood region simulation and visualisation; 4.5.3 Adequacy of using the Wald confidence region; 4.6 Data analysis; 4.7 Discussion; References; 5 Mixture of experts modelling with social science applications; 5.1 Introduction; 5.2 Motivating examples; 5.2.1 Voting blocs; 5.2.2 Social and organisational structure; 5.3 Mixture models
5.4 Mixture of experts models
Record Nr. UNINA-9910809170003321
Chichester, West Sussex, : Wiley, 2011
Materiale a stampa
Lo trovi qui: Univ. Federico II
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Response surfaces, mixtures, and ridge analyses [[electronic resource] /] / George E.P. Box, Norman R. Draper
Response surfaces, mixtures, and ridge analyses [[electronic resource] /] / George E.P. Box, Norman R. Draper
Autore Box George E. P
Edizione [2nd ed.]
Pubbl/distr/stampa Hoboken, N.J., : John Wiley, c2007
Descrizione fisica 1 online resource (873 p.)
Disciplina 519.57
Altri autori (Persone) DraperNorman Richard
Collana Wiley Series in Probability and Statistics
Soggetto topico Experimental design
Response surfaces (Statistics)
Mixture distributions (Probability theory)
Ridge regression (Statistics)
Soggetto genere / forma Electronic books.
ISBN 1-282-24228-8
9786613813404
0-470-07276-8
0-470-07275-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Response Surfaces, Mixtures, and Ridge Analyses; Contents; Preface to the Second Edition; 1. Introduction to Response Surface Methodology; 1.1. Response Surface Methodology (RSM); 1.2. Indeterminancy of Experimentation; 1.3. Iterative Nature of the Experimental Learning Process; 1.4. Some Classes of Problems (Which, How, Why); 1.5. Need for Experimental Design; 1.6. Geometric Representation of Response Relationships; 1.7. Three Kinds of Applications; 2. The Use Of Graduating Functions; 2.1. Approximating Response Functions; 2.2. An Example; Appendix 2A. A Theoretical Response Function
3. Least Squares for Response Surface Work3.1. The Method of Least Squares; 3.2. Linear Models; 3.3. Matrix Formulas for Least Squares; 3.4. Geometry of Least Squares; 3.5. Analysis of Variance for One Regressor; 3.6. Least Squares for Two Regressors; 3.7. Geometry of the Analysis of Variance for Two Regressors; 3.8. Orthogonalizing the Second Regressor, Extra Sum of Squares Principle; 3.9. Generalization to p Regressors; 3.10. Bias in Least-Squares Estimators Arising from an Inadequate Model; 3.11. Pure Error and Lack of Fit; 3.12. Confidence Intervals and Confidence Regions
3.13. Robust Estimation, Maximum Likelihood, and Least SquaresAppendix 3A. Iteratively Reweighted Least Squares; Appendix 3B. Justification of Least Squares by the Gauss-Markov Theorem; Robustness; Appendix 3C. Matrix Theory; Appendix 3D. Nonlinear Estimation; Appendix 3E. Results Involving V(y); Exercises; 4. Factorial Designs at Two Levels; 4.1. The Value of Factorial Designs; 4.2. Two-Level Factorials; 4.3. A 2(6) Design Used in a Study of Dyestuffs Manufacture; 4.4. Diagnostic Checking of the Fitted Models, 2(6) Dyestuffs Example; 4.5. Response Surface Analysis of the 2(6) Design Data
Appendix 4A. Yates' Method for Obtaining the Factorial Effects for a Two-Level DesignAppendix 4B. Normal Plots on Probability Paper; Appendix 4C. Confidence Regions for Contour Planes (see Section 4.5); Exercises; 5. Blocking and Fractionating 2(k) Factorial Designs; 5.1. Blocking the 2(6) Design; 5.2. Fractionating the 2(6) Design; 5.3. Resolution of a 2(k-p) Factorial Design; 5.4. Construction of 2(k-p) Designs of Resolution III and IV; 5.5. Combination of Designs from the Same Family; 5.6. Screening, Using 2(k-p) Designs (Involving Projections to Lower Dimensions)
5.7. Complete Factorials Within Fractional Factorial Designs5.8. Plackett and Burman Designs for n = 12 to 60 (but not 52); 5.9. Screening, Using Plackett and Burman Designs (Involving Projections to Lower Dimensions); 5.10. Efficient Estimation of Main Effects and Two-Factor Interactions Using Relatively Small Two-Level Designs; 5.11. Designs of Resolution V and of Higher Resolution; 5.12. Application of Fractional Factorial Designs to Response Surface Methodology; 5.13. Plotting Effects from Fractional Factorials on Probability Paper; Exercises
6. The Use of Steepest Ascent to Achieve Process Improvement
Record Nr. UNINA-9910143691403321
Box George E. P  
Hoboken, N.J., : John Wiley, c2007
Materiale a stampa
Lo trovi qui: Univ. Federico II
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