Testing if a mixture is from a given location–scale family

References

• Everitt , B. S. and Hand , D. J. 1981 . Finite Mixture Distributions , London : Chapman and Hall .
   Google Scholar
• Titterington , D. M. , Smith , A. F.M. and Makov , U. E. 1985 . Statistical Analysis of Finite Mixture Distributions , New York : Wiley and Sons .
   Google Scholar
• McLachlan , G. J. and Basford , K. E. 1988 . Mixture Models: Inference and Applications to Clustering , New York : Marcel Dekker .
   Google Scholar
• Gelman , A. , Carlin , J. B. , Stern , H. S. and Rubin , D. B. 1995 . Bayesian Data Analysis , London : Chapman and Hall .
   Google Scholar
• Böhning , D. 1999 . Computer-assisted Analysis of Mixtures and Applications: Meta-analysis, Disease Mapping and Others , Boca Raton , FL : Chapman and Hall/CRC .
   Google Scholar
• McLachlan , G. J. and Peel , D. 2000 . Finite Mixture Models , New York : John Wiley and Sons .
   Google Scholar
• Koski , T. 2001 . Hidden Markov Models for Bioinformatics , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Cornell , J. A. 2002 . Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data , 3 , New York : Wiley and Sons .
   Google Scholar
• Prabhakar Murthy , D. N. , Xie , M. and Jiang , R. 2004 . Weibull Models , Hoboken , NJ : John Wiley and Sons .
   Google Scholar
• Frühwirth-Schnatter , S. 2006 . Finite Mixture and Markov Switching Models , New York : Springer Verlag .
   Google Scholar
• Press , W. H. , Teukolsky , S. A. , Vetterling , W. T. and Flannery , B. P. 2007 . Numerical Recipes: The Art of Scientific Computing , 3 , Cambridge : Cambridge University Press .
   Google Scholar
• Pons , O. 2009 . Estimation and Testing in Models of Mixtures of Distributions and Change-points , Paris : Hermes Science Publications/Lavoisier .
   Google Scholar
• Suckling , J. , Sigmundsson , T. , Greenwood , K. and Bullmore , E. T. 1999 . A modified fuzzy clustering algorithm for operator independent brain tissue classification of dual echo MR images . Magn. Reson. Imaging , 17 : 1065 – 1076 . (doi:10.1016/S0730-725X(99)00055-7)
   PubMed Web of Science ®Google Scholar
• Ane , T. and Labidi , C. 2001 . Revisiting the finite mixture of Gaussian distributions with application to futures markets . J. Futures Markets , 21 : 347 – 376 . (doi:10.1002/1096-9934(200104)21:4<347::AID-FUT3>3.0.CO;2-T)
   Web of Science ®Google Scholar
• Tentoni , S. , Astolfi , P. , De Pasquale , A. and Zonta , L. A. 2004 . Birthweight by gestational age in preterm babies according to a Gaussian mixture model . BJOG , 111 : 31 – 37 . (doi:10.1046/j.1471-0528.2003.00006.x)
   PubMed Web of Science ®Google Scholar
• Chantler , E. , Abraham-Peskir , J. and Roberts , C. 2004 . Consistent presence of two normally distributed sperm subpopulations within normozoospermic human semen: A kinematic study . Int. J. Androl. , 27 : 350 – 359 . (doi:10.1111/j.1365-2605.2004.00498.x)
   PubMed Web of Science ®Google Scholar
• Kennedy , N. , Everitt , B. , Boydell , J. , Van Os , J. , Jones , P. B. and Murray , R. M. 2005 . Incidence and distribution of first-episode mania by age: Results from a 35-year study . Psychol. Med. , 35 : 855 – 863 . (doi:10.1017/S0033291704003307)
   PubMed Web of Science ®Google Scholar
• McLachlan , G. J. , Bean , R. W. and Jones , L. B.T. 2006 . A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays . Bioinformatics , 22 : 1608 – 1615 . (doi:10.1093/bioinformatics/btl148)
   PubMed Web of Science ®Google Scholar
• Alexander , C. and Lazar , E. 2006 . Normal mixture GARCH(1,1): Applications to exchange rate modelling . J. Appl. Econ. , 21 : 307 – 336 . (doi:10.1002/jae.849)
   Web of Science ®Google Scholar
• Agarwal , D. 2007 . Detecting anomalies in cross-classified streams: A Bayesian approach . Knowl. Inf. Syst. , 11 : 29 – 44 . (doi:10.1007/s10115-006-0036-4)
   Web of Science ®Google Scholar
• Boettcher , P. J. , Caraviello , D. and Gianola , D. 2007 . Genetic analysis of somatic cell scores in US Holsteins with a Bayesian mixture model . J. Dairy Sci. , 90 : 435 – 443 . (doi:10.3168/jds.S0022-0302(07)72645-0)
   PubMed Web of Science ®Google Scholar
• Ertel , A. and Tozeren , A. 2008 . Switch-like genes populate cell communication pathways and are enriched for extracellular proteins . BMC Genomics , 9 : 3 (doi:10.1186/1471-2164-9-3)
   PubMed Web of Science ®Google Scholar
• Wang , M. and Chen , J. Y. 2010 . A GMM-IG framework for selecting genes as expression panel biomarkers . Artif. Intell. Med. , 48 : 75 – 82 . (doi:10.1016/j.artmed.2009.07.006)
   PubMed Web of Science ®Google Scholar
• Linden , M. 2001 . A model for stock return distribution . Int. J. Finance Econ. , 6 : 159 – 169 . (doi:10.1002/ijfe.149)
   Web of Science ®Google Scholar
• Bohacek , S. and Rozovskii , B. 2004 . A diffusion model of roundtrip time . Comput. Stat. Data Anal. , 45 : 25 – 50 . (doi:10.1016/S0167-9473(03)00114-2)
   Web of Science ®Google Scholar
• Ananthasayanam , M. R. , Anilkumar , A. K. and Rao , P. V.S. 2006 . A new stochastic impressionistic low Earth model of the space debris scenario . Acta Astronaut. , 59 : 547 – 559 . (doi:10.1016/j.actaastro.2006.04.003)
   Web of Science ®Google Scholar
• Bhowmick , D. , Davison , A. C. , Goldstein , D. R. and Ruffieux , Y. 2006 . A Laplace mixture model for identification of differential expression in microarray experiments . Biostatistics , 7 : 630 – 641 . (doi:10.1093/biostatistics/kxj032)
   PubMed Web of Science ®Google Scholar
• Cord , A. , Ambroise , C. and Cocquerez , J. P. 2006 . Feature selection in robust clustering based on Laplace mixture . Pattern Recognit. Lett. , 27 : 627 – 635 . (doi:10.1016/j.patrec.2005.09.028)
   Web of Science ®Google Scholar
• Suzuki , Y. and Shibata , T. 2007 . Hardware architecture for pseudo-two-dimensional hidden-Markov-model-based face recognition systems employing Laplace distribution functions . Jpn. J. Appl. Phys. Part 1 – Regular Papers Brief Communications and Review Papers , 46 : 2265 – 2270 . (doi:10.1143/JJAP.46.2265)
   Web of Science ®Google Scholar
• Rabbani , H. and Vafadust , M. 2008 . Image/video denoising based on a mixture of Laplace distributions with local parameters in multidimensional complex wavelet domain . Signal Process. , 88 : 158 – 173 . (doi:10.1016/j.sigpro.2007.07.016)
   Web of Science ®Google Scholar
• Anilkumar , A. K. and Reddy , D. S. 2009 . Statistical conjunction analysis and modeling of low-earth-orbit catalogued objects . J. Spacecr. Rockets , 46 : 160 – 167 . (doi:10.2514/1.36976)
   Web of Science ®Google Scholar
• Chen , C. L. and Yu , K. M. 2009 . Automatic Bayesian quantile regression curve fitting . Stat. Comput. , 19 : 271 – 281 . (doi:10.1007/s11222-008-9091-x)
   Web of Science ®Google Scholar
• Manas , A. 2009 . French butchers don't do quantum physics . Econom. Lett. , 103 : 101 – 106 . (doi:10.1016/j.econlet.2009.02.009)
   Web of Science ®Google Scholar
• Feenstra , B. and Skovgaard , Ib. M. 2004 . A quantitative trait locus mixture model that avoids spurious LOD score peaks . Genetics , 167 : 959 – 965 . (doi:10.1534/genetics.103.025437)
   PubMed Web of Science ®Google Scholar
• Anderson , W. F. , Pfeiffer , R. M. , Dores , G. M. and Sherman , M. E. 2006 . Comparison of age distribution patterns for different histopathologic types of breast carcinoma . Cancer Epidemiol. Biomarkers Prev. , 15 : 1899 – 1905 . (doi:10.1158/1055-9965.EPI-06-0191)
   PubMed Web of Science ®Google Scholar
• Soyer , R. and Xu , F. 2010 . Assessment of mortgage default risk via Bayesian reliability models . Appl. Stoch. Models Bus. Ind. , 26 : 308 – 330 . (doi:10.1002/asmb.849)
   Web of Science ®Google Scholar
• Trott , M. 2006 . The Mathematica GuideBook for Symbolics , New York : Springer Verlag .
   Google Scholar
• Withers , C. S. 1991 . Moment estimates for mixtures with common scale . Comm. Statist. Theory Methods , 20 : 1445 – 1461 . (doi:10.1080/03610929108830576)
   Web of Science ®Google Scholar
• Walker , R. J. 1950 . Algebraic Curves , Princeton , NJ : Princeton University Press .
   Google Scholar
• Barnard , S. and Child , J. M. 1952 . Higher Algebra , London : Macmillan .
   Google Scholar
• Azzalini , A. 1985 . A class of distributions which includes the normal ones . Scand. J. Statist. , 12 : 171 – 178 .
   Web of Science ®Google Scholar
• Azzalini , A. 1986 . Further results on a class of distributions which includes the normal ones . Statistica , 46 : 199 – 208 .
   Google Scholar
• Marsaglia , G. , Tsang , W. W. and Wang , J. 2003 . Evaluating Kolmogorov's distribution . J. Statist. Softw. , 8 : 1 – 4 .
   Google Scholar
• Brinkman , N. D. 1981 . Ethanol fuel – a single-cylinder engine study of efficiency and exhaust emissions . SAE Transactions , 68 paper number 810345.
   Google Scholar
• Hurn , M. , Justel , A. and Robert , C. P. 2003 . Estimating mixtures of regressions . J. Comput. Graph. Statist. , 12 : 55 – 79 . (doi:10.1198/1061860031329)
   Web of Science ®Google Scholar
• Pena , D. , Rodriguez , J. and Tiao , G. C. 2003 . Identifying mixtures of regression equations by the SAR procedure . Bayesian Statist. , 7 : 327 – 347 .
   Google Scholar
• Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics , London : Chapman and Hall .
   Google Scholar
• Blom , G. 1958 . Statistical Estimates and Transformed Beta-variables , New York : Wiley and Sons .
   Google Scholar
• Chambers , J. , Cleveland , W. , Kleiner , B. and Tukey , P. 1983 . Graphical Methods for Data Analysis , London : Chapman and Hall .
   Google Scholar
• Kendall , M. G. and Stuart , A. 1977 . The Advanced Theory of Statistics , 4 , Vol. 1 , London : Griffin .
   Google Scholar