The content of the program has been structured into three blocks:
The Block I (point 1), devoted to the descriptive statistics, whose aim is to provide the student knowledge and understanding of the basic concepts of descriptive statistics of data sets univariate and bivariate analyzes. These concepts include measures of centralization, dispersion and form, basic graphics as histograms and boxplots, and scatter diagrams correlating with correlation coefficients and with linear regression.
In the Block II (points 2,3 and 4), dedicated to the probability and ramdom variables, we will provide the student with knowledge of probability and one-dimensional random variables and its moments, with emphasis on the binomial distributions, negative binomial, geometric, Poisson, Pareto, uniform, normal, log-normal, Student's t test, chi-square, gamma, exponential, Weibull and beta. There are knowledge and understanding of dimensional variables, and basic concepts, as well as on linear combinations of random variables. Concludes with the study of the Central Limit Theorem.
In the Block III (points 5-6), dedicated to the Statistical inference, introduces the concept of sampling distribution to derive conclusions on one (or two) population (s) unknown (s). This target is achieved by means of the calculation of intervals of confidence, the parametric hypothesis contrast for one or two populations, and the nonparametric hypothesis contrast hypothesis of goodness of fit and independence. There becomes special emphasis on the concepts of p-value and potency of the contrast of hypothesis introduced. The last topic is related to Simulation (Monte Carlo and bootstrap methods) and applications.
Each topic exercises must be conducted using the R software.
Topic 1: Introduction. Descriptive statistics.
1.1. Probability and Statistics in the areas of insurance and finance.
1.2. Descriptive statistics for univariate and bivariate data.
1.3. Measures of centralization, dispersion and form, basic graphics as histograms and boxplots, and diagrams of dispersion.
1.4. Correlation and linear regression.
1.5. Examples with R.
Topic 2: Concepts of probability.
2.1. Review of concepts of probability.
2.2. Conditional probability and Bayes theorem.
2.3. Examples with R.
Topic 3: Random variables.
3.1. One-dimensional random variables.
3.2. Discrete and continuous random variables.
3.3. Random vectors. Transformations of random variables.
3.4. Central limit theorem.
3.6. Two dimensional Variables and related concepts.
3.7. Jointly distributed random variables and conditional distributions.
3.8. Concept of independence
3.9. Examples with R.
Topic 4: Useful probability distributions in actuarial practice.
4.1. Geometric, negative binomial, binomial distributions, Poisson distribution.
4.2. Pareto, uniform, normal, log-normal, Student, Chi-square, exponential, gamma t beta and Weibull distribition.
4.3. Examples in R.
Topic 5: Review of statistical inference and its actuarial and financial implementation.
5.1. Point estimation and confidence intervals.
5.2. Parametric and nonparametric hypothesis contrasts.
5.3. Examples in R.
Topic 6: Simulation.
6.1. Explain the concepts simulation. Monte Carlo simulation.
6.2. Simulate both discrete and continuous random variables.
6.3. Estimate the number of simulations needed to obtain an estimate with a given error and a given degree of confidence.
6.4. Bootstrap method. Use the bootstrap method to estimate properties (e.g. the mean squared error) of an estimator.
6.5. Examples in R.