| Statistică matematică | Mathematical statistics |
trul |
|||||
(Mathematics-Computer Science) |
|||||
(Computer Science) |
|||||
(Mathematics) |
| Cadre didactice indrumatoare | Teaching Staff in Charge |
| Prof. Dr. BLAGA Petru, pblaga@cs.ubbcluj.ro Prof. Dr. MIHOC Ion, imihoc@math.ubbcluj.ro Lect. SOOS Anna, asoos@math.ubbcluj.ro |
| Obiective | Aims |
|
Insusirea cunostintelor fundamentale ale statisticii matematice. Se urmareste latura aplicativa a acestora precum si familiarizarea studentilor cu utilizarea calculatorului si a produselor informatice existente. |
The use of the basic facts of the Statistics theory for some applications and the use of software in Statistics. |
|
1. Statistica descriptiva. Indicatori statistici. Culegere, reprezentarea si prelucrarea datelor statistice. Distributie statistica. Parametrii distributiilor statistice (medie, dispersie, mediana, cuantile, corelatie, coeficient de corelatie, regresie).
2. Teoria selectiei. Sondaje. Functii de selectie. Medie de selectie. Dispersie de selectie. Moment de selectie. Moment centrat de selectie. Functie de repartitie de selectie. Teorema lui Glivenko. Teorema lui Kolmogorov. Criteriul lui Kolmogorov. 3. Teoria estimatiei. Functii de estimatie. Estimatori absolut corecti si estimatori corecti. Statistici suficiente. cantitatea de informatie a lui Fischer. Inegalitatea Rao-Cramer. Metode de estimare a parametrilor (metoda momentelor, metoda verosimitatii maxime, metoda minimului X2, metoda intervalelor de incredere, metoda intervalelor pentru selectii mari). 4. Verificarea ipotezelor statistice. Teste pentru verificarea ipotezelor statistice. Regiune critica. Puterea unui test. Eroare de genul I si eroare de genul II. Lema Neyman-Pearson. Testul Z si testul T (Student) privind media teoretica. Testul raportului verosimilitatilor. Testul Hi2 privind dispersia teoretica. Testul F (Snedecor-Fischer) pentru compararea dispersiilor. Teste pentru compararea mediilor. Testul Hi2 pentru compararea mai multor caracteristici. Testul Hi2 pentru tabele de contigenta. Testul de concordanta Kolmogorov-Smirnov. |
|
1. Blaga, P., Statistical methods in modelling by computer (Romanian). Universitatea ";Babes--Bolya" Press, Cluj-Napoca, 1993.
2. Blaga, P., Probability theory and mathematical statistics, Vol. II. (Romanian), Universitatea "Babes--Bolyai" Press, Cluj-Napoca, 1994. 3. Blaga, P., Mathematical statistics. Practical activities (Romanian), Universitatea "Babes--Bolyai" Press, Cluj-Napoca, 1999. 4. Blaga, P., Mathematical statistics. (Romanian), Universitatea "Babes--Bolyai" Press, Cluj-Napoca, 2000. 5. Blaga, P., Muresan, A.S., Applied mathematics in economics, Vol. I. (Romanian), Transilvania Press, Cluj--Napoca, 1996. 6. Ciucu, G., Probability theory and mathematical statistics. (Romanian), DP Press, Bucharest, 1963. 7. Ciucu, G., Craiu, V., Theory of estimation and testing statistical hypotheses (Romanian), DP Press, Bucharest, 1968. 8. Ciucu, G., Craiu, V., Introduction to probability theory and mathematical statistics (Romanian), DP Press, Bucharest, 1971. 8. Ciucu, G., Craiu, V., Statistical inference (Romanian), DP Press, Bucharest, 1974. 9. Craiu, V., Testing statistical hypotheses (Romanian), SE Press, Bucharest, 1972. 10.Cramer, H., Mathematical methods of statistics, Princeton University Press, Princeton, 1951 11.Hoel, P.J., Introduction to mathematical statistics, Fourth edition, John Wiley & Sons, New York-London-Sydney-Toronto}, 1971. 12.Hoel, P. J., Statistique mathematique, Tome II, Armand Colin Press, Paris, 1991. 13.Iosifescu, M., Mihoc, Gh., Theodorescu, R., Probability theory and mathematical statistics (Romanian), Tech. Press, Bucharest, 1966. 14.Kendall, M. G., Stuart, A., The advanced theory of statistics. Vol. 1. Distribution theory, Second edition , Charles Griffin & Company Limited, London, 1963. 15.Kendall, M. G., Stuart, A., The advanced theory of statistics. Vol. 2. Inference and relationship, Charles Griffin & Company Limited, London, 1961. 16.Kendall, M. G., Stuart, A., The advanced theory of statistics. Vol. 3. Design and analysis, and time-series, Charles Griffin & Company Limited, London, 1966. 17.Mihoc, Gh., Ciucu, G., Craiu, V., Probability theory and mathematical statistics (Romanian), DP Press, Bucharest, 1970. 18.Saporta, G., Probabilites, analyse des donnees et statistique, Editions Technip, Paris, 1990. 19.Snedecor, G. W., Cochran, W. G., Statistical methods, Iowa State University Press, 1989. 20.Tassi, Ph., Methodes statistiques, Economica, Paris, 1989. 21.Yule, G. U., Kendall, M. G., Introduction to the theory of statistics (Romanian), Sci. Press, Bucharest, 1969. |
| Evaluare | Assessment |
|
Examen. |
Exam. |