## "Babes-Bolyai" University of Cluj-Napoca Faculty of Mathematics and Computer Science

 Mathematical statistics
 Code Semes-ter Hours: C+S+L Credits Type Section MC015 7 2+1+0 5 compulsory Matematica Economica MC015 7 2+1+0 5 compulsory Matematici Aplicate
 Teaching Staff in Charge
 Prof. BLAGA Petru, Ph.D., pblaga@cs.ubbcluj.roLect. SOOS Anna, Ph.D., asoos@math.ubbcluj.ro
 Aims Knowledge of basic concepts and methods of mathematical statistics. The applied side of mathematical statistics and implements on computers of some methods of mathematical statistics are followed.
 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, 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.
 Assessment Exam.