Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MC004 Mathematical Statistics
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
7
2+2+1
compulsory
Mathematics-Computer Science
7
2+2+1
compulsory
Applied Mathematics
7
2+2+1
compulsory
Teaching Staff in Charge
Prof. AGRATINI Octavian, Ph.D.,  agratinimath.ubbcluj.ro
Assoc.Prof. SOOS Anna, Ph.D.,  asoosmath.ubbcluj.ro
Lect. LISEI Hannelore-Inge, Ph.D.,  hannemath.ubbcluj.ro
Aims
The use of the basic facts of the Statistics theory for some applications and the use of software in Statistics.
Content
1. Descriptive statistics:
Classification of data. Graphical representation of empirical distributions. Empirical moments. Empirical correlation and regression (Pearson, Spearman, Kendall, Friedman coefficients, regression problem, linear and non-linear regression, least squares method).
2. Sampling theory: Random sampling. Sampling functions. Mean. Variance. Standard deviation. Moments. Corrections for grouping. Correlation coefficient. Exact sampling distributions (Fisher's lemma, Student distribution, chi-square distribution, Fisher-Snedecor distribution). Asymptotic properties of sampling distributions (Gnedenko, and Kolomogorov theorems).
3. Theory of estimation: Estimators and estimations. Consistency. Point estimators. Unbiased estmator. Biased estimator. Sufficiency. Fisher's information. Rao-Cramer inequality. Minimum variance estimators. Efficiency. Methods of estimations (method of moments, method of maximum likelihood, confidence intervals method).
4. Testing statistical hypotheses: Simple and composite hypotheses, parametric and non-parametric tests. Power of statistical test. Test of simple hypotheses. Neymann's lemma. Most powerful test. Test of composite hypotheses. Testing of mean and difference of two means(Z-test, T-test). Testing of variance and ratio of two variances(chi-square-test, F-test). Chi-square test (multinomial distribution, goodness of fit, contingency tables, homogenity). Non-parametric tests (Kolmogorov test, Kolmogorov-Smirnov test).
References
1. BLAGA, PETRU: Calculul probabilităţilor şi statistică matematică. Vol.II. Curs şi culegere de probleme. Cluj-Napoca: Universitatea "Babeş-Bolyai" Cluj-Napoca, 1994.
2. BLAGA, PETRU: Statistică matematică. Lucrări de laborator. Cluj-Napoca: Universitatea "Babeş-Bolyai" Cluj-Napoca, 1999.
3. BLAGA, PETRU: Statistică... prin Matlab. Cluj-Napoca: Presa Universitară Clujeană, 2002.
4. CIUCU, G. - CRAIU, V.: Introducere în teoria probabilităţilor şi statistică matematică. Bucureşti: Editura Didactică şi Pedagogică, 1971.
5. CIUCU, G. - CRAIU, V.: Inferenţă statistică. Bucureşti: Editura Didactică şi Pedagogică, 1974.
6. IOSIFESCU, M. - MIHOC, GH. - THEODORESCU, R.: Teoria probabilităţilor şi statistică matematică. Bucuresti: Editura Tehnică, 1966.
7. LEHMANN, E.L.: Testing statistical hypotheses. New York: Springer, 1997.
8. SCHERVISH, M.J.: Theory of statistics. New York: Springer, 1995.
9. SAPORTA, G.: Probabilités, analyse des données et statistique. Paris: Editions Technip, 1990.
10.TRÎMBIŢAŞ, RADU T.: Metode statistice. Cluj-Napoca: Presa Universitară Clujeană, 2000.
Assessment
Exam.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject