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  • STATISTICS
  • Summary
  • Thanks
**In Progress**
Goal
The goal of this guide is to help you understand the Fundamental concepts in Statistics.
  • First, we will see the underlying (theoretical) idea behind the concept.
  • Then we will visualize that concept (at https://app.quantml.org/statistics/ ).
  • Then we will use programming language Python  ,  Julia    to fill the holes and fully grasp that concept.
Resources
Table for CDF of
\(\mathcal{N}(0,1)=\Phi(x)\)
\(\bullet\)
  Online Calculator to calculate Area under the
\(\text{Gaussian Distribution }\mathcal{N}(\mu,\sigma^2)\)


Table of Content

  • \(1)\)
    Introduction      
    Launch pythonjulia
    • \(1.1\)
           Goals
    • \(1.2\)
           What is statistics?
    • \(1.3\)
           Probability
    • \(1.4\)
           Statistical Modeling
    • \(1.5\)
           The Counting Balls Example
    • \(1.6\)
           Statistical Experiment
    • \(1.7\)
           Estimator
    • \(1.8\)
           Modeling assumptions
        • Python Simulation
          \(1)\)
          The Counting Balls Example
          \(2)\)
          Multiple Simulations
        Julia Simulation
          \(1)\)
          The Counting Balls Example
          \(2)\)
          Multiple Simulations
  • \(2)\)
    Weak Law of Large Numbers      
    Launch pythonjulia
    • \(2.1\)
           Law of Large Numbers
    • \(2.2\)
           Gamblers Fallacy
        • Python Simulation
          \(1)\)
          Single Simulation
          \(2)\)
          Multiple Simulations
        Julia Simulation
          \(1)\)
          Single Simulation
          \(2)\)
          Multiple Simulations
  • \(3)\)
    Central Limit Theorem      
    Launch pythonjulia
    • \(3.1\)
           Introduction
      • \(3.1.1\)
             Sampling Distribution of the Mean
    • \(3.2\)
           Convergence of Sampling Distribution
    • \(3.3\)
           Rate of Convergence
        • Python Simulation
          \(1)\)
          Single Simulation
          \(2)\)
          Multiple Simulations
        Julia Simulation
          \(1)\)
          Single Simulation
          \(2)\)
          Multiple Simulations
  • \(4)\)
    Gaussian Distribution      
    Launch pythonjulia
    • \(4.1\)
           Introduction
    • \(4.2\)
           Properties of Gaussian
      • 🔸 Python Implementation
      🔹 Julia Implementation
  • \(5)\)
    Modes of Convergence      
    • Coming Soon

    • Topics to be covered

    • • Inference
      • • Estimation
      • • Confidence Intervals
      • • Hypothesis testing
    • • Statistical modelling
    • • Identifiability
    • • Bias, Variance and Quadratic Risk
    • • Confidence Interval
    • • Delta Method
    • • Hypothesis Testing
      • • Hypothesis testing
      • • One Sample Test
      • • Two Sample Test
      • •
        \(\text{p-value}\)
    • • Statistical Test
      • • Statistical Test
        \((\psi)\)
      • • Rejection Region
      • • Type
        \(1\)
        error of a test
        \((\psi)\)
      • • Type
        \(2\)
        error of a test
        \((\psi)\)
      • • Power of a test
        \((\psi)\)
      • • Level
    • • Total Variation Distance
    • • Kullback-Leibler (KL) Divergence
    • • Maximum Likelihood Estimator
    • • Covariance Matrices
    • • Fisher Information
    • • Method of Moments
    • • M-estimation
    • • The Chi-Squared Distribution
    • • Student's T Distribution
    • • The Student's T Test (T Test)
    • • Wald's Test
    • • Likelihood Ratio Test
    • • Goodness of Fit Tests
    • • Kolmogorov-Smirnov Test
    • • Kolmogorov-Lilliefors Test
    • • Quantile-Quantile (QQ) Plots
    • • Introduction to the Bayesian Framework
    • • Jeffreys Prior
    • • Linear/Ridge Regression
    • • Generalized Linear Models; Exponential Families
      • • Introduction to GLM
      • • Link Function
      • • Link Function
      • • Canonical Link Function
      • • GLM Statistical Model

      The above list can be expanded i.e. more topics can be added.


**In Progress**