Welcome to xtremes’ documentation!

xtremes is a Python library for various utilities useful in Extreme Value Statistics. So far, you will find tools to fit more than one order statistics for parameter estimation as well as a Bootstrap device.

It is created within the ClimXtreme project and will provide supplementary code and simulations for the papers yet to come.

Check out the Usage section for further information, including how to Installation the project.

Note

This project is under active and heavy development.

Chapters

• Usage
  • Installation
  • The modules
• Time Series and Extreme Value Analysis
  • Step 1: Simulating Time Series Data
  • Step 2: Extracting Block Maxima
  • Step 3: Extracting High Order Statistics
  • Step 4: Estimating Parameters with PWM
  • Step 5: Maximum Likelihood Estimation (MLE)
  • Step 6: Analyzing Real Data
  • Conclusion
• Bootstrap and MLE Tutorial
  • Step 1: Block Maxima Extraction
  • Step 2: Bootstrapping a Sample
  • Step 3: Aggregating the Bootstrap Sample
  • Step 4: Maximum Likelihood Estimation (MLE)
  • Step 5: Running Full Bootstrap for MLE
  • Conclusion
• Bias Correction Tutorial
  • Step 1: Generating Block Indices
  • Step 2: Computing Exceedances
  • Step 3: Estimating Cluster Size Probability
  • Step 4: Using Bias Correction Functions
  • Step 5: Solving for Bias-Corrected Parameters
  • Conclusion
• Utility Functions for Extreme Value Analysis
  • Step 1: Using the Sigmoid and Inverse Sigmoid Functions
  • Step 2: Calculating Probability Weighted Moments (PWM)
  • Step 3: Estimating GEV Parameters from PWM
  • Step 4: Working with the GEV Distribution
  • Step 5: Simulating Time Series Data
  • Conclusion
• Reference: topt
  • Overview
  • Classes
  • The TimeSeries Class and its Functionalities
  • Examples
  • The HighOrderStats Class and its Functionalities
  • Examples
  • The Data Class and its Functionalities
  • The PWM_estimators Class
  • The ML_estimators, Frechet_ML_estimators and ML_estimators_data Classes
  • Running Extensive Simulations
  • Examples
• Reference: Bootstrap
  • Overview
  • Classes
  • The FullBootstrap Class
  • Functions
  • The circmax Function
  • The uniquening Function
  • The Bootstrap Function
  • The aggregate_boot Function
  • The bootstrap_worker Function
  • Examples
  • References
• Reference: Miscellaneous
  • Overview
  • Basic Functions
  • Examples
  • The GEV and its Likelihood
  • Examples
  • Piece Wise Moment Estimation
  • Examples
  • Simulating Time Series
  • Examples
• Bias Correction
  • Overview
  • Functions
  • The I_sb Function
  • The D_n Function
  • The exceedances Function
  • The hat_pi0 Function
  • The Upsilon Function
  • The Upsilon_derivative Function
  • The Upsilon_2ndderivative Function
  • The Psi Function
  • The a1_asy Function
  • The varpi Function
  • The z0 Function