Statistical Analysis of Extremes: Risk Measures & Inference

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Quantitative Risk Management: Risk Measures

Covers risk measures used in determining risk capital and insurance premiums.

Precipitation and Hydrologic Design

Covers methods to define the design storm, empirical distribution of rainfall maxima, Gumbel distribution, and intensity-duration-frequency relationships.

Extreme Values: Applications and Probability Framework

Explores extreme values in random variables, applications in environmental factors, reliability modeling, block maxima distribution, and the Generalized Extreme Value distribution.

Risk Measures and Multivariate Distributions

Covers risk measures, VaR, ES computation, backtesting, and multivariate distributions for portfolio risk assessment.

Data Analysis: Correlation Measures

Covers the basics of data analysis, focusing on statistical concepts and correlation measures.

Statistical Inference: Confidence Intervals

Covers the construction of approximate confidence intervals using the central limit theorem for large sample sizes.

Extreme Value Analysis: Statistical Consequences

Explores the statistical consequences of extreme value analysis and implications of model mis-specification.

Weibull Model: Random Data

Explores the Weibull model's application to random data and its significance in analyzing material strength and failure probability.

L-Moment Estimation: Probability-Weighted Moments

Covers L-moment estimation, probability-weighted moments, and maximum likelihood inference basics.

Optimality in Statistical Inference

Delves into the duality between confidence intervals and hypothesis tests, emphasizing the importance of precision and accuracy in estimation.