| Title:
|
On numerical evaluation of maximum-likelihood estimates for finite mixtures of distributions (English) |
| Author:
|
Grim, Jiří |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
18 |
| Issue:
|
3 |
| Year:
|
1982 |
| Pages:
|
173-190 |
| . |
| Category:
|
math |
| . |
| MSC:
|
62F10 |
| MSC:
|
62F12 |
| MSC:
|
65C99 |
| idZBL:
|
Zbl 0489.62028 |
| idMR:
|
MR680154 |
| . |
| Date available:
|
2009-09-24T17:27:26Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124132 |
| . |
| Reference:
|
[1] C. A. Aйвазян З. И. Бежаева O. В. Cтароверов: Kлассификация многомерных наблюдений.(Classification of Multivariate Observations). Статистика, Mocквa 1974. Zbl 0341.10006 |
| Reference:
|
[2] H. H. Aпраушева: Алгоритм расщепления смеси нормальных классов.(Algorithm for resolution of a mixture of normal classes). C6. Программы и алгоритмы (1976), 68. Zbl 1079.34527 |
| Reference:
|
[3] H. H. Aпраушева: Определение числа классов в задачах классификации I.(Determination of the number of classes in classification problems I). Известия AH CCCP - Teх. kибернетика (1981), 3, 71-77. Zbl 1024.00503, MR 0691559 |
| Reference:
|
[4] J. Behboodian: On a mixture of normal distributions.Biometrika 57 (1970), 1, 215-217. Zbl 0193.18104 |
| Reference:
|
[5] C. G. Bhattacharya: A simple method of resolution of a distribution into Gaussian components.Biometrics 23 (1967), 115-137. |
| Reference:
|
[6] W. R. Blischke: Moment estimators for the parameters of a mixture of two binomial distributions.Ann. Math. Statist. 33 (1962), 2, 444-454. Zbl 0131.17804, MR 0137219 |
| Reference:
|
[7] W. R. Blischke: Mixtures of distributions.In: Classical and Contagious Discrete Distributions (G. P. Patil, ed.), Pergamon Press, New York 1963. |
| Reference:
|
[8] W. R. Blischke: Estimating the parameters of mixtures of binomial distributions.J. Amer. Statist. Assoc. 59 (1964), 306, 510-528. Zbl 0128.13501, MR 0162310 |
| Reference:
|
[9] C. Bürrau: The half-invariants of the sum of two typical laws of errors with an application to the problem of dissecting a frequency curve into components.Scand. Actuar. J. 77 (1934), 1, 1-5. |
| Reference:
|
[10] C. V. L. Charlier: Researches into the theory of probability.Meddelanden fran Lunds Astron. Observ. (1906) Sec. 2, Bd. 1. |
| Reference:
|
[11] A. C. Cohen: Discussion of "Estimation of parameters for a mixture of normal distributions" by Victor Hasselblad.Technometrics 8 (1966), 3, 445-446. MR 0196842 |
| Reference:
|
[12] A. C. Cohen: Estimation in mixtures of two normal distributions.Technometrics 9 (1967), 15-28. Zbl 0147.18104, MR 0216626 |
| Reference:
|
[13] P. W. Cooper: Some topics on nonsupervised adaptive detection for multivariate normal distributions.In: Computer and Information Sciences - II. (J. T. Tou, ed.), Academic Press, New York 1967. Zbl 0214.47205 |
| Reference:
|
[14] N. E. Day: Estimating the components of a mixture of normal distributions.Biometrika 56 (1969), 463-474. Zbl 0183.48106, MR 0254956 |
| Reference:
|
[15] N. P. Dick D. C. Bowden: Maximum likelihood estimation for mixtures of two normal distributions.Biometrics 29 (1973), 4, 781 - 790. |
| Reference:
|
[16] G. Doetsch: Zerlegung einer Funktion in Gaussche Fehlerkurven und zeitliche Zurückverfolgung eines Temperaturzustandes.Math. Z. 41 (1936), 283 - 318. MR 1545619 |
| Reference:
|
[17] R. O. Duda P. E. Hart: Pattern Classification and Scene Analysis.John Wiley, New York-London 1973. |
| Reference:
|
[18] E. B. Fowlkes: Some methods for studying the mixture of two normal (lognormal) distributions.J. Amer. Statist. Assoc. 74 (1979), 367, 561-575. Zbl 0434.62024 |
| Reference:
|
[19] J. G. Fryer C. A. Roberston: A comparison of some methods of estimating mixed normal distributions.Biometrika 59 (1972), 639-648. MR 0339387 |
| Reference:
|
[20] N. T. Gridgeman: A comparison of two methods of analysis of normal distributions.Technometrics 12 (1970), 4, 832-833. |
| Reference:
|
[21] J. Grim: Metody shlukové analýzy a jejich využití při zpětnovazebním řízení velkých systému.(Methods of cluster analysis and their application for feedback control of large systems). Dissertation, Institute of Information Theory and Automation, Prague 1979. |
| Reference:
|
[22] J. Grim: An algorithm for maximizing a finite sum of positive functions and its application to cluster analysis.Problems of Control and Information Theory 10 (1981), 6, 427-437. Zbl 0476.65100, MR 0643728 |
| Reference:
|
[23] E. J. Gumbel: La dissection d'une repartition.Annales de l'Université de Lyon 3 (1939), 39-51. Zbl 0063.01784 |
| Reference:
|
[24] A. K. Gupta T. Miyawaki: On uniform mixture model.Biometrical J. 20 (1978), 631 - 637. MR 0530762 |
| Reference:
|
[25] L. F. Guseman J. R. Walton: Methods for estimating proportions of convex combinations of normals using linear feature selection.Comm. Statist. A - Theory Methods A7 (1978), 1439-1450. |
| Reference:
|
[26] V. Hasselblad: Estimation of parameters for a mixture of normal distributions.Technometrics 8 (1966), 431-444. MR 0196842 |
| Reference:
|
[27] V. Hasselblad: Finite mixtures of distributions from the exponential family.Ph. D. Dissertation University of California, Los Angeles 1967. |
| Reference:
|
[28] V. Hasselblad: Estimation of finite mixtures of distributions from the exponential family.J. Amer. Statist. Assoc. 64 (1969), 328, 1459-1471. |
| Reference:
|
[29] B. M. Hill: Information for estimating the proportions in mixtures of exponential and normal distributions.J. Amer. Statist. Assoc. 58 (1963), 918-932. MR 0155381 |
| Reference:
|
[30] D. W. Hosmer: A comparison of iterative maximum likelihood estimates of the parameters of a mixture of two normal distributions under three different types of samples.Biometrics 29 (1973), 761-770. |
| Reference:
|
[31] D. W. Hosmer: A use of mixtures of two normal distributions in a classification problem.J. Statist. Comput. Simulation 6 (1978), 384, 281-294. Zbl 0381.62051 |
| Reference:
|
[32] D. W. Hosmer N. P. Dick: Information and mixtures of two normal distributions.J. Statist. Comput. Simulation 6 (1977), 137-148. |
| Reference:
|
[33] O. К. Исаенко К. Ю. Ypбax: Разделение смесей распределений вероятностей на их составляюшие.(Decomposition of mixtures of probability distributions into their components). Теория вероятностей и математическая статистика, теор. кибернетика, том 13, 37-58, ВИНИТИ, Mocквa 1976. |
| Reference:
|
[34] I. R. James: Estimation of the mixing proportion in a mixture of two normal distributions from simple rapid measurements.Biometrics 34 (1978), 2, 265-275. Zbl 0384.62027 |
| Reference:
|
[35] E. John: Bayesian estimation of mixture distributions.Ann. Math. Statist, 39 (1968), 4, 1289-1302. MR 0229334 |
| Reference:
|
[36] B. K. Kale: On the solution of likelihood equations by iteration processes: The multiparametric case.Biometrika 49 (1962), 479-486. Zbl 0118.14301, MR 0156403 |
| Reference:
|
[37] R. Kanno: Estimation of parameters for a mixture of two normal distributions.Rep. Statist. Appl. Res. JUSE 22 (1975), 4, 1-15. Zbl 0356.62024, MR 0420954 |
| Reference:
|
[38] S. Kullback: An information-theoretic derivation of certain limit relations for a stationary Markov Chain.SIAM J. Control 4 (1966), 3, 454-459. Zbl 0199.21301, MR 0203804 |
| Reference:
|
[39] S. Kullback: Information Theory and Statistics.Wiley, New York-Dover 1968. MR 0103557 |
| Reference:
|
[40] P. D. M. Macdonald: Estimation of finite distribution mixtures.In: Applied Statistics (R. P. Gupta, ed.), North-Holland 1975. Zbl 0303.62023, MR 0408087 |
| Reference:
|
[41] P. Medgyessy: Decomposition of Superpositions of Density Functions and Discrete Distributions.Akadémiai Kiadó, Budapest 1977. Zbl 0363.60013, MR 0438428 |
| Reference:
|
[42] G. Meeden: Bayes estimation of the mixing distributions, the discrete case.Ann. Math. Statist. 43 (1972), 6, 1993-1999. MR 0350943 |
| Reference:
|
[43] W. Molenaar: Survey of estimation methods for a mixture of two normal distributions.Statist. Neerlandica 19 (1965), 4, 249-265. MR 0196844 |
| Reference:
|
[44] G. D. Murray D. M. Titterington: Estimation problems with data from a mixture.Appl. Statist. 27(1978), 3, 325-334. |
| Reference:
|
[45] K. Pearson: Contributions to the mathematical theory of evolution 1: Dissection of frequency curves.Philos. Trans. Roy. Soc. London Ser. A 185 (1894), 71-110. |
| Reference:
|
[46] B. C. Peters W. A. Coberly: The numerical evaluation of the maximum-likelihood estimate of mixture proportions.Comm. Statist. A - Theory Methods A5 (1976), 12, 1127-1135. MR 0433687 |
| Reference:
|
[47] B. C. Peters H. F. Walker: An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions.SIAM J. Appl. Math. 35 (1978), 2, 362-378. MR 0518877 |
| Reference:
|
[48] B. C. Peters H. F. Walker: The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions.SIAM J. Appl. Math. 35 (1978), 3,447-452. MR 0507946 |
| Reference:
|
[49] J. G. Postaire C. P. A. Vasseur: An approximate solution to normal mixture identification with application to unsupervised pattern classification.IEEE Trans, on Pattern Analysis & Machine Intelligence PAMI-3 (1981), 2, 163-179. |
| Reference:
|
[50] R. E. Quandt J. B. Ramsey: Estimating mixtures of normal distributions and switching regressions.J. Amer. Statist. Assoc. 73 (1978), 364, 730-752. MR 0521324 |
| Reference:
|
[51] C. R. Rao: Advanced Statistical Methods in Biometric Research.John Wiley and Sons, New York 1952. Zbl 0047.38601, MR 0050824 |
| Reference:
|
[52] P. R. Rider: The method of moments applied to a mixture of two exponential distributions.Ann. Math. Statist. 32 (1961), 1, 143-147. Zbl 0106.13101, MR 0119282 |
| Reference:
|
[53] W. Schilling: A frequency distribution represented as the sum of two Poisson distributions.J. Amer. Statist. Assoc. 42 (1947), 407-424. MR 0021280 |
| Reference:
|
[54] D. F. Stanat: Unsupervised learning of mixtures of probability functions.In: Pattern Recognition (L. Kanal, ed.), Thompson Book Co., Washington D. C. 1968, 357-389. |
| Reference:
|
[55] B. Stromgren: Tables and diagrams for dissecting a frequency curve into components by the half-invariant method.Scand. Actuar. J. 17 (1934), 1, 7-54. |
| Reference:
|
[56] M. И. Шлезингер: Взаимосвязъ обучения и самообучения в разпознавании образов.(Relation between learning and self-learning in pattern recognition). Кивернетика (Kиев) (1968), 2, 81-88. Zbl 1099.01025 |
| Reference:
|
[57] W. Y. Tan W. C. Chang: Some comparisons of the method of moments and the method of maximum likelihood in estimating parameters of a mixture of two normal densities.J. Amer. Statist. Assoc. (57(1972), 339, 702-708. |
| Reference:
|
[58] H. F. Walker: Estimating the proportions of two populations in a mixture using linear maps.Comm. Statist. A - Theory Methods A9 (1980), 8, 837-849. Zbl 0437.62019, MR 0573116 |
| Reference:
|
[59] J. H. Wolfe: A computer program for the maximum likelihood analysis of types.(Technical Bulletin 65-15), U.S. Naval Personnel Research Activity, San Diego 1965. |
| Reference:
|
[60] J. H. Wolfe: NORMIX: computational methods for estimating the parameters of multivariate normal mixtures of distributions.(Research Memorandum SRM 68-2), U.S. Naval Personnel Research Activity, San Diego 1967. |
| Reference:
|
[61] J. H. Wolfe: Pattern clustering by multivariate mixture analysis.Multivariate Behavioral Research 5 (1970), July, 329-350. |
| Reference:
|
[62] S. J. Yakowitz: Unsupervised learning and the identification of finite mixtures.IEEE Trans. Inform. Theory IT- 16 (1970), 5, 330-338. Zbl 0197.45502 |
| Reference:
|
[63] T. Y. Young G. Coraluppi: Stochastic estimation of a mixture of normal density functions using an information criterion.IEEE Trans. Inform. Theory IT-16 (1970), 258-263. |
| . |
