Descriptive Statistics and Probability (BM Statistics)
Content of the Lecture
Introduction
- Population
- Variables
- Scales of Measure
Analysis of One-Dimensional Data
- Univariate Frequency Distribution
- Discrete and Continous Classified Data
- Cumulative Distribution Function
- Quantiles
- Box Plot
- Measures of Location
- Mode
- Median
- Arithmetic Mean
- Aggregation Theorem for Means
- Trimmed Arithmetic Mean
- Measures of Dispersion
- Range
- Interquartile Range
- Variance
- Standard Deviation
- Variance Decomposition
- Gini Mean Difference
Measurement of Concentration and Inequality
- Curve of Concentration
- Rosenbluth Index
- Herfindahl Index
- Lorenz Curve
- Gini Coefficient
- Coefficient of Variation
Indices
- Index Types: Laspeyres Indices, Paasche Indices and Fisher Indices
- Index Numbers: Price Indices, Volume Indices and Value Indices
- Aggregation of Subindices
- Consumer Price Indices
Analysis of Multidimensional Data
- Marginal Distribution
- Conditionial Distribution
- Descriptive Independence
- Covariance
- Coefficient of Correlation
- Spearman’s Rank Correlation Coefficient
- Pearson’s Contingency Coefficient
Random Experiments and Probability
- Random Experiments
- Sample Space
- Events and their Linkage
- Probabilities
- Formal Definition of Probability
- Laplace Experiments
- Basic Rules of Probability and Combinatorics
- Conditional Probability
- Conditional Probability
- Total Probability and Bayes' Theorem
- Independence of Events
Random Variables and Distributions
- Random Variables
- Cumulative Distribution Function
- Quantile Function
- Discrete Random Variables
- Continuous Random Variables
- Affine-Linear Transformation of Random Variables
- Distribution Parameter
- Expected Value
- Variance
- Tchebychev Inequality