Syllabus
Event, probability, the axioms of probability, conditional probability, Bayes´theorem.
Frequency, class intervals, histograms, percentiles, boxplots. Measures of locations (mean, trimmed mean, trimean, median, mode), measures of spread (sample variance, sample standard deviation, trimmed variance, interquartile range), robustness. Intersequential variability. Moments of the distribution, measures of skewness and curtosis. Power transformations, standardized anomalies. Sample covariance, correlation (Pearson correlation, Spearman rank correlation), robustness.
Random variables, distribution function, discrete and continuous random variables, probability density function, expectation, variance, moments and central moments, Continuous distributions - uniform distribution, normal (Gaussian) distribution, lognormal, gamma, beta, distribution, chí-distribution, Students´ distribution, the F distribution, Gumbel, Weibull, GEV. Discrete distributions - binomial distribution, Poisson distribution. Multivariate distributions, bivariate normal distribution. Covariance, correlation.
Tchebycheff's inequality, the law of large numbers, the central limit theorem.
Criteria of estimation (consistency, unbiasedness, efficiency). Maximum-likelihood estimation, moments estimation. Qualitative assessments of the goodness of fit (probability plots, P-P plot, Q-Q plot). Confidence intervals. Parametric and nonparametric tests, the concept of statistical tests ("null" hypothesis, "alternative" hypothesis, one-sided and two-sided test, test statistic, type I and type II error, the significance level of a test, the power of a test). One-sample tests (test for a population mean, Chi-square test for a population variance), limitations, tests of two sample means (under independence, for paired variables, under serial dependence), tests of variances. Tests of normality. Tests of the correlation coefficient, Fisher's z-transformation. Nonparametric tests (sign tests, one-sample and two-sample Wilcoxon rank tests, tests for paired samples). Goodness of fit tests (Kolmogorov-Smirnov, Chi-square test). Contingency tables.
Simple regression model, assumptions, limitation, least square regression parameter estimates. Analysis of variance, coefficient of determination, tests and confidence intervals for the regression parameters.
Annotation
Introduction to statistical analysis: Probability, random variables, descriptive statistics, probability distributions, parameters estimation, confidence intervals, hypothesis testing, correlations and linear regression.