Universitatea "Babes-Bolyai" Cluj-Napoca
Facultatea de Matematica si Informatica
FISA DISCIPLINEI

Statistică matematică
Cod
Semes-
trul
Ore: C+S+L
Credite
Tipul
Sectia
MC015
7
2+1+0
5
obligatorie
Matematica Economica
MC015
7
2+1+0
5
obligatorie
Matematici Aplicate
Cadre didactice indrumatoare
Prof. Dr. BLAGA Petru, pblaga@cs.ubbcluj.ro
Lect. Dr. SOOS Anna, asoos@math.ubbcluj.ro
Obiective
Cunoasterea notiunilor de baza si a metodelor statisticii matematice. Se urmareste latura aplicativa a statisticii matematice si implementarea pe calculator a unor metode ale statisticii matematice.
Continut
Notiuni de baza ale teoriei selectiei. Distributii de selectie. Caracteristici ale distributiilor de selectie (medie de selectie, dispersie de selectie, momente de selectie, mediana, cuantile, asimetrie, exces, coeficent de corelatie - Pearson, Spearman, Kendall). Teorema lui Glivenko, teoremele lui Kolmogorov si Smirnov. Notiuni de baza ale teoriei estimatiei. Estimatori punctuali. Nedeplasare. Consistenta. Eficienta. Suficienta. Inegalitatea Rao-Cramer. Metode de estimatie: metoda momentelor, metoda verosimilitatii maxime, metoda celor mai mici patrate. Estimatori nepunctuali: intervale de incredere, regiuni de incredere. Verificarea ipotezelor statistice. Erori de genul intai si de genul al doilea. Cele mai puternice teste. Teste relative la valoarea medie teoretica: testul Z si testul T. Teste privind diferenta a doua medii teoretice. Test privind raportul a doua dispersii teoretice (testul F). Teste privind concordanta (distributia multinomiala, densitatea de probabilitate, tabele de contingenta, omogenitate). Teste neparametrice (testul semnelor, testul sumei rangurilor, testul lui Kolmogorov, testul Kolmogorov-Smirnov).
Bibliografie
1. Blaga, P., Statistical methods in modelling by computer (Romanian). Universitatea "Babes--Bolyai" 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
Examen.