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

Mathematical statistics
Hours: C+S+L
Matematica Economica
Matematici Aplicate
Teaching Staff in Charge
Prof. BLAGA Petru, Ph.D., pblaga@cs.ubbcluj.ro
Lect. SOOS Anna, Ph.D., asoos@math.ubbcluj.ro
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.
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)
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