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

SUBJECT

Code
Subject
MMP0002 Mathematical Statistics
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
5
2+2+1
speciality
compulsory
Mathematics and Computer Science
5
2+2+1
speciality
compulsory
Applied Mathematics
5
2+2+1
speciality
compulsory
Teaching Staff in Charge
Assoc.Prof. LISEI Hannelore-Inge, Ph.D.,  hannemath.ubbcluj.ro
Assoc.Prof. SOOS Anna, Ph.D.,  asoosmath.ubbcluj.ro
Asist. ROSCA Natalia Carmen, Ph.D.,  nataliamath.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