Topic 1: Introduction. Review of concepts.
1.1. Descriptive statistics. Correlation and linear regression.
1.2. Probability concepts. Random variables. Central Limit Theorem. Statistical dependence and independence.
1.3. Probability distributions useful in actuarial practice. Binomial, Negative Binomial, Geometric, Poisson, Pareto, Uniform, Normal, log-Normal, Student's t, Chi-square, Gamma, Exponential, Beta and Weibull distributions, among others.
1.4. Exercises and practical applications in R.
Topic 2: Statistical inference and its actuarial and financial application.
2.1. Non-parametric estimation. Kernel estimation, adjustment and validation methods.
2.2. Parametric Estimation. Method of Moments, Maximum Likelihood and Percentile Matching method. Confidence Intervals and Hypothesis Tests.
2.3. Exercises and practical applications in R.
Topic 3: Statistical techniques and their application in insurance.
3.1. Risk measures.
3.2. Calculation of probabilities. Simulation of scenarios. Cross-validation.
3.3. Aggregate models.
3.4. Optimisation algorithms.
3.5. Practical applications in R.