Statistics-and-Probability-in-Python
说明： Python中的统计学和概率论，探索“统计学”和“概率论”的概念及其在“Python”中的实现，
(Explore "Statistics" and "Probability Theory" Concepts and Their Implementations in "Python" ,)
(Explore "Statistics" and "Probability Theory" Concepts and Their Implementations in "Python" ,)
文件列表:
Chapter 1 Special Continuous Random Variables.ipynb (1551352, 2023-01-06)
Chapter 2 Special Discrete Random Variables.ipynb (652841, 2023-01-06)
Chapter 3 Confidence Intervals.ipynb (75027, 2023-01-06)
Chapter 4 Parametric Hypothesis Testing.ipynb (94304, 2023-01-06)
Chapter 5 Statistical Hypothesis Testing.ipynb (40685, 2023-01-06)
Chapter 6 Regression.ipynb (271441, 2023-01-06)
Chapter 7 Analysis of Variance (Anova).ipynb (33244, 2023-01-06)
LICENSE (35149, 2023-01-06)
Chapter 2 Special Discrete Random Variables.ipynb (652841, 2023-01-06)
Chapter 3 Confidence Intervals.ipynb (75027, 2023-01-06)
Chapter 4 Parametric Hypothesis Testing.ipynb (94304, 2023-01-06)
Chapter 5 Statistical Hypothesis Testing.ipynb (40685, 2023-01-06)
Chapter 6 Regression.ipynb (271441, 2023-01-06)
Chapter 7 Analysis of Variance (Anova).ipynb (33244, 2023-01-06)
LICENSE (35149, 2023-01-06)
# Statistics and Probability in Python “ “  
> **`Note`**: This repository is still developing.
[](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%201%20Special%20Continuous%20Random%20Variables.ipynb)
- 1.1. Normal (Gaussian) Distribution
- 1.2. Chi-square Distribution
- 1.3. T-student Distribution
- 1.4. Fisher Distribution
- 1.5. Continuous Uniform Distribution
- 1.6. Exponential Distribution
- 1.7. Gamma Distribution
- 1.8. Beta Distribution
- 1.9. Weibull Distribution
- 1.10. Cauchy Distribution
- 1.11. Laplace Distribution
**Chapter 2: Special Discrete Random Variables** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%202%20Special%20Discrete%20Random%20Variables.ipynb)
- 2.1. Bernoulli Distribution
- 2.2. Binomial Distribution
- 2.3. Negative Binomial (Pascal) Distribution
- 2.4. Geometric Distribution
- 2.5. Poisson Distribution
- 2.6. Discrete Uniform Distribution
- 2.7. Hypergeometric Distribution
**Chapter 3: Confidence Intervals** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%203%20Confidence%20Intervals.ipynb)
- 3.1. Confidence Interval for the Mean of a Normal Population
- 3.1.1. Known Standard Deviation
- 3.1.2. Unknown Standard Deviation
- 3.2. Confidence Interval for the Variance of a Normal Population
- 3.2.1. Unknown Mean of the Population
- 3.2.2. Known Mean of the Population
- 3.3. Confidence Interval for the Difference in Means of Two Normal Population
- 3.3.1. Known Variances
- 3.3.2. Unknown but Equal Variances
- 3.4. Confidence Interval for the Ratio of Variances of Two Normal Populations
- 3.5. Confidence Interval for the Mean of a Bernoulli Random Variable
**Chapter 4: Parametric Hypothesis Testing** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%204%20Parametric%20Hypothesis%20Testing.ipynb)
- 4.1. Introduction
- 4.2. Test Concerning the Mean of a Normal Population
- 4.2.1. Known Standard Deviation
- 4.2.2. Unknown Standard Deviation
- 4.3. Test Concerning the Equality of Means of Two Normal Populations
- 4.3.1. Known Variances
- 4.3.2. Unknown but Equal Variances
- 4.4. Paired t-test
- 4.5. Test Concerning the Variance of a Normal Population
- 4.6. Test Concerning the Equality of Variances of Two Normal Populations
- 4.7. Test Concerning P in Bernoulli Populations
- 4.8. Test Concerning the Equality of P in Two Bernoulli Populations
**Chapter 5: Statistical Hypothesis Testing** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%205%20Statistical%20Hypothesis%20Testing.ipynb)
- 5.1. Normality Tests
- 5.1.1. Shapiro-Wilk Test
- 5.1.2. DAgostinos Test
- 5.1.3. Anderson-Darling Test
- 5.2. Correlation Tests
- 5.2.1. Pearsons Correlation Coefficient
- 5.2.2. Spearmans Rank Correlation
- 5.2.3. Kendalls Rank Correlation
- 5.2.4. Chi-Squared Test
- 5.3. Stationary Tests
- 5.3.1. Augmented Dickey-Fuller Unit Root Test
- 5.3.2. Kwiatkowski-Phillips-Schmidt-Shin Test
- 5.4. Other Tests
- 5.4.1. Mann-Whitney U-Test
- 5.4.2. Wilcoxon Signed-Rank Test
- 5.4.3. Kruskal-Wallis H Test
- 5.4.4. Friedman Test
**Chapter 6: Regression** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%206%20Regression.ipynb)
- 6.1. Introduction
- 6.2. Least Squares Estimators of the Regression Parameters
- 6.3. Statistical Inferences about the Regression Parameters
- 6.3.1. Inferences Concerning B
- 6.3.1.1. Known Variance
- 6.3.1.2. Unknown Variance
- 6.3.2. Inferences Concerning A
- 6.3.2.1. Unknown Variance
- 6.3.3. T-tests for Regression Parameters with statsmodels
- 6.3.4. F-statistic for Overall Significance in Regression
- ***. Confidence Intervals Concerning Regression Models
- ***.1. Confidence Interval for B
- ***.1.1. Known Variance
- ***.1.2. Unknown Variance
- ***.2. Confidence Interval for A
- ***.2.1. Unknown Variance
- ***.3. Confidence Interval for A+Bx
- ***.3.1. Unknown Variance
- ***.4. Prediction Interval of a Future Response
- 6.5. Residuals
- 6.5.1. Regression Diagnostic
- 6.5.2. Multicolinearity
**Chapter 7: Analysis of Variance (ANOVA)** [](http://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%207%20Analysis%20of%20Variance%20%28Anova%29.ipynb)
- 7.1. One-Way Analysis of Variance
- 7.1.1. Equal Sample Sizes
- 7.1.2. Unequal Sample Sizes
- 7.2. Two-Way Analysis of Variance
[](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%201%20Special%20Continuous%20Random%20Variables.ipynb)
- 1.1. Normal (Gaussian) Distribution
- 1.2. Chi-square Distribution
- 1.3. T-student Distribution
- 1.4. Fisher Distribution
- 1.5. Continuous Uniform Distribution
- 1.6. Exponential Distribution
- 1.7. Gamma Distribution
- 1.8. Beta Distribution
- 1.9. Weibull Distribution
- 1.10. Cauchy Distribution
- 1.11. Laplace Distribution
**Chapter 2: Special Discrete Random Variables** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%202%20Special%20Discrete%20Random%20Variables.ipynb)
- 2.1. Bernoulli Distribution
- 2.2. Binomial Distribution
- 2.3. Negative Binomial (Pascal) Distribution
- 2.4. Geometric Distribution
- 2.5. Poisson Distribution
- 2.6. Discrete Uniform Distribution
- 2.7. Hypergeometric Distribution
**Chapter 3: Confidence Intervals** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%203%20Confidence%20Intervals.ipynb)
- 3.1. Confidence Interval for the Mean of a Normal Population
- 3.1.1. Known Standard Deviation
- 3.1.2. Unknown Standard Deviation
- 3.2. Confidence Interval for the Variance of a Normal Population
- 3.2.1. Unknown Mean of the Population
- 3.2.2. Known Mean of the Population
- 3.3. Confidence Interval for the Difference in Means of Two Normal Population
- 3.3.1. Known Variances
- 3.3.2. Unknown but Equal Variances
- 3.4. Confidence Interval for the Ratio of Variances of Two Normal Populations
- 3.5. Confidence Interval for the Mean of a Bernoulli Random Variable
**Chapter 4: Parametric Hypothesis Testing** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%204%20Parametric%20Hypothesis%20Testing.ipynb)
- 4.1. Introduction
- 4.2. Test Concerning the Mean of a Normal Population
- 4.2.1. Known Standard Deviation
- 4.2.2. Unknown Standard Deviation
- 4.3. Test Concerning the Equality of Means of Two Normal Populations
- 4.3.1. Known Variances
- 4.3.2. Unknown but Equal Variances
- 4.4. Paired t-test
- 4.5. Test Concerning the Variance of a Normal Population
- 4.6. Test Concerning the Equality of Variances of Two Normal Populations
- 4.7. Test Concerning P in Bernoulli Populations
- 4.8. Test Concerning the Equality of P in Two Bernoulli Populations
**Chapter 5: Statistical Hypothesis Testing** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%205%20Statistical%20Hypothesis%20Testing.ipynb)
- 5.1. Normality Tests
- 5.1.1. Shapiro-Wilk Test
- 5.1.2. DAgostinos Test
- 5.1.3. Anderson-Darling Test
- 5.2. Correlation Tests
- 5.2.1. Pearsons Correlation Coefficient
- 5.2.2. Spearmans Rank Correlation
- 5.2.3. Kendalls Rank Correlation
- 5.2.4. Chi-Squared Test
- 5.3. Stationary Tests
- 5.3.1. Augmented Dickey-Fuller Unit Root Test
- 5.3.2. Kwiatkowski-Phillips-Schmidt-Shin Test
- 5.4. Other Tests
- 5.4.1. Mann-Whitney U-Test
- 5.4.2. Wilcoxon Signed-Rank Test
- 5.4.3. Kruskal-Wallis H Test
- 5.4.4. Friedman Test
**Chapter 6: Regression** [](https://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%206%20Regression.ipynb)
- 6.1. Introduction
- 6.2. Least Squares Estimators of the Regression Parameters
- 6.3. Statistical Inferences about the Regression Parameters
- 6.3.1. Inferences Concerning B
- 6.3.1.1. Known Variance
- 6.3.1.2. Unknown Variance
- 6.3.2. Inferences Concerning A
- 6.3.2.1. Unknown Variance
- 6.3.3. T-tests for Regression Parameters with statsmodels
- 6.3.4. F-statistic for Overall Significance in Regression
- ***. Confidence Intervals Concerning Regression Models
- ***.1. Confidence Interval for B
- ***.1.1. Known Variance
- ***.1.2. Unknown Variance
- ***.2. Confidence Interval for A
- ***.2.1. Unknown Variance
- ***.3. Confidence Interval for A+Bx
- ***.3.1. Unknown Variance
- ***.4. Prediction Interval of a Future Response
- 6.5. Residuals
- 6.5.1. Regression Diagnostic
- 6.5.2. Multicolinearity
**Chapter 7: Analysis of Variance (ANOVA)** [](http://nbviewer.org/github/Pegah-Ardehkhani/Statistics-and-Probability-in-Python/blob/main/Chapter%207%20Analysis%20of%20Variance%20%28Anova%29.ipynb)
- 7.1. One-Way Analysis of Variance
- 7.1.1. Equal Sample Sizes
- 7.1.2. Unequal Sample Sizes
- 7.2. Two-Way Analysis of Variance
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