2. Basic statistical elements

Abstract

This chapter is introducing the very basic statistical operations that can be done using the Uranie platform, on a set of points provided by the user, or generated by Uranie itself.

This chapter introduces the various probability laws implemented in Uranie and illustrates, for each every one of them, with a few sets of parameters, the resulting shape of three of their characteristic functions. Some of the basic statistical operations are also described in a second part.

• 2.1. Random variable modelisation
  • 2.1.1. The probability distributions
    • 2.1.1.1. Uniform Law
    • 2.1.1.2. Log Uniform Law
    • 2.1.1.3. Triangular Law
    • 2.1.1.4. LogTriangular Law
    • 2.1.1.5. Normal law
    • 2.1.1.6. LogNormal law
    • 2.1.1.7. Trapezium law
    • 2.1.1.8. UniformByParts law
    • 2.1.1.9. Exponential law
    • 2.1.1.10. Cauchy law
    • 2.1.1.11. GumbelMax law
    • 2.1.1.12. Weibull law
    • 2.1.1.13. Beta law
    • 2.1.1.14. GenPareto law
    • 2.1.1.15. Gamma law
    • 2.1.1.16. InvGamma law
    • 2.1.1.17. Student Law
    • 2.1.1.18. Generalized normal law
    • 2.1.1.19. Composing law
• 2.2. Statistical treatments and operations
  • 2.2.1. Normalising the variable
  • 2.2.2. Computing the ranking
  • 2.2.3. Computing the elementary statistic
  • 2.2.4. The quantile computation
    • 2.2.4.1. Empirical computation
    • 2.2.4.2. Wilks-quantile computation
  • 2.2.5. Correlation matrix
• 2.3. Combining these aspects: performing PCA
  • 2.3.1. Theoretical introduction
    • 2.3.1.1. Purpose
    • 2.3.1.2. Implementation in a nutshell
    • 2.3.1.3. Limitation of PCA