115 lines
7.4 KiB
Markdown
115 lines
7.4 KiB
Markdown
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# Statistics and Probability in Python 📊 📈  
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> **`Note`**: This repository is still developing.
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<p align="center">
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<img width="500" height="350" src="https://cdn.dribbble.com/users/962944/screenshots/14138307/media/ca3377660c3d2053c9d91ac175871429.gif">
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</p>
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## Table of content ✍️
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**Chapter 1: Special Continuous Random Variables** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%201%20Special%20Continuous%20Random%20Variables.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%201%20Special%20Continuous%20Random%20Variables.ipynb)
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- 1.1. Normal (Gaussian) Distribution
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- 1.2. Chi-square Distribution
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- 1.3. T-student Distribution
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- 1.4. Fisher Distribution
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- 1.5. Continuous Uniform Distribution
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- 1.6. Exponential Distribution
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- 1.7. Gamma Distribution
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- 1.8. Beta Distribution
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- 1.9. Weibull Distribution
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- 1.10. Cauchy Distribution
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- 1.11. Laplace Distribution
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**Chapter 2: Special Discrete Random Variables** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%202%20Special%20Discrete%20Random%20Variables.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%202%20Special%20Discrete%20Random%20Variables.ipynb)
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- 2.1. Bernoulli Distribution
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- 2.2. Binomial Distribution
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- 2.3. Negative Binomial (Pascal) Distribution
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- 2.4. Geometric Distribution
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- 2.5. Poisson Distribution
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- 2.6. Discrete Uniform Distribution
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- 2.7. Hypergeometric Distribution
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**Chapter 3: Confidence Intervals** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%203%20Confidence%20Intervals.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%203%20Confidence%20Intervals.ipynb)
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- 3.1. Confidence Interval for the Mean of a Normal Population
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- 3.1.1. Known Standard Deviation
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- 3.1.2. Unknown Standard Deviation
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- 3.2. Confidence Interval for the Variance of a Normal Population
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- 3.2.1. Unknown Mean of the Population
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- 3.2.2. Known Mean of the Population
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- 3.3. Confidence Interval for the Difference in Means of Two Normal Population
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- 3.3.1. Known Variances
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- 3.3.2. Unknown but Equal Variances
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- 3.4. Confidence Interval for the Ratio of Variances of Two Normal Populations
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- 3.5. Confidence Interval for the Mean of a Bernoulli Random Variable
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**Chapter 4: Parametric Hypothesis Testing** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%204%20Parametric%20Hypothesis%20Testing.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%204%20Parametric%20Hypothesis%20Testing.ipynb)
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- 4.1. Introduction
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- 4.2. Test Concerning the Mean of a Normal Population
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- 4.2.1. Known Standard Deviation
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- 4.2.2. Unknown Standard Deviation
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- 4.3. Test Concerning the Equality of Means of Two Normal Populations
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- 4.3.1. Known Variances
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- 4.3.2. Unknown but Equal Variances
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- 4.4. Paired t-test
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- 4.5. Test Concerning the Variance of a Normal Population
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- 4.6. Test Concerning the Equality of Variances of Two Normal Populations
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- 4.7. Test Concerning P in Bernoulli Populations
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- 4.8. Test Concerning the Equality of P in Two Bernoulli Populations
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**Chapter 5: Statistical Hypothesis Testing** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%205%20Statistical%20Hypothesis%20Testing.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%205%20Statistical%20Hypothesis%20Testing.ipynb)
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- 5.1. Normality Tests
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- 5.1.1. Shapiro-Wilk Test
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- 5.1.2. D’Agostino’s Test
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- 5.1.3. Anderson-Darling Test
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- 5.2. Correlation Tests
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- 5.2.1. Pearson’s Correlation Coefficient
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- 5.2.2. Spearman’s Rank Correlation
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- 5.2.3. Kendall’s Rank Correlation
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- 5.2.4. Chi-Squared Test
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- 5.3. Stationary Tests
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- 5.3.1. Augmented Dickey-Fuller Unit Root Test
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- 5.3.2. Kwiatkowski-Phillips-Schmidt-Shin Test
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- 5.4. Other Tests
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- 5.4.1. Mann-Whitney U-Test
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- 5.4.2. Wilcoxon Signed-Rank Test
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- 5.4.3. Kruskal-Wallis H Test
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- 5.4.4. Friedman Test
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**Chapter 6: Regression** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%206%20Regression.ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%206%20Regression.ipynb)
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- 6.1. Introduction
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- 6.2. Least Squares Estimators of the Regression Parameters
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- 6.3. Statistical Inferences about the Regression Parameters
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- 6.3.1. Inferences Concerning B
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- 6.3.1.1. Known Variance
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- 6.3.1.2. Unknown Variance
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- 6.3.2. Inferences Concerning A
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- 6.3.2.1. Unknown Variance
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- 6.3.3. T-tests for Regression Parameters with statsmodels
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- 6.3.4. F-statistic for Overall Significance in Regression
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- 6.4. Confidence Intervals Concerning Regression Models
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- 6.4.1. Confidence Interval for B
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- 6.4.1.1. Known Variance
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- 6.4.1.2. Unknown Variance
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- 6.4.2. Confidence Interval for A
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- 6.4.2.1. Unknown Variance
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- 6.4.3. Confidence Interval for A+Bx
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- 6.4.3.1. Unknown Variance
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- 6.4.4. Prediction Interval of a Future Response
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- 6.5. Residuals
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- 6.5.1. Regression Diagnostic
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- 6.5.2. Multicolinearity
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**Chapter 7: Analysis of Variance (ANOVA)** <a href="https://colab.research.google.com/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%207%20Analysis%20of%20Variance%20(Anova).ipynb" target="_parent\"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a> [](http://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%207%20Analysis%20of%20Variance%20%28Anova%29.ipynb)
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- 7.1. One-Way Analysis of Variance
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- 7.1.1. Equal Sample Sizes
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- 7.1.2. Unequal Sample Sizes
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- 7.2. Two-Way Analysis of Variance
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