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所在平台: Udemy |
课程主页: https://www.udemy.com/course/statistics-moments-skewness-kurtosis-and-correlation/
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《人工智能统计学基础》课程总结 本课程旨在为人工智能领域的学习者提供坚实的统计学基础。课程内容涵盖了统计学中的多个核心概念，并着重于其在统计学、经济学、精算科学以及人工智能中的应用。 课程开篇介绍了**矩（Moments）**的概念，包括如何计算数据点和频率分布的四种中心矩。随后深入讲解了**偏度（Skewness）**，定义了偏度为衡量分布对称性的指标，并详细介绍了两种主要的偏度系数计算方法：**卡尔·皮尔逊偏度系数（Karl Pearson's coefficient of skewness）**和**鲍利偏度系数（Bowley's coefficient of skewness）**。课程通过实际计算示例，展示了如何处理频率分布数据来计算这些系数。 紧接着，课程引入了**峰度（Kurtosis）**，将其定义为衡量频率曲线形状的指标，并区分了三种类型的峰度曲线：正态峰、尖峰和扁峰。通过计算中心矩，课程演示了如何根据分布的峰度特征进行判断。 课程的最后部分聚焦于**相关性（Correlation）**和**秩相关（Rank Correlation）**。首先介绍了**协方差（Covariance）**的概念及其计算方法，随后讲解了**皮尔逊相关系数（Karl Pearson's coefficient of Correlation）**，如何利用协方差和变量方差计算相关系数。此外，课程还教授了**斯皮尔曼秩相关系数（Spearman's Rank Correlation coefficient）**的计算方法，以及在处理重复排名数据时的注意事项。 在实践应用方面，课程还包括了均值、中位数、众数等基本统计量的练习。此外，课程还为学习者提供了**推论统计学（Inferential Statistics）**的入门介绍，涵盖了样本均值、样本比例、样本标准差等基本术语，以及**区间估计（Interval Estimation）**的概念，包括置信区间和置信值的计算，特别是在计算总体均值和总体比例的区间估计时。 课程最后部分对**假设检验（Hypothesis Testing）**进行了阐述，介绍了原假设、接受或拒绝假设的参数，并详细讲解了**t分布（t distributions）**，包括如何查表和使用t值来接受或拒绝假设，以及**双尾t检验（two tailed t test）**。 总而言之，本课程提供了从基础统计概念到推论统计方法的全面讲解，旨在帮助学习者掌握统计学知识，为在人工智能及相关领域的深入学习打下坚实基础。
Bringing you more learning in Statistics through this course. The target audience could be students of Applied Mathematics or Statistics, or anyone interested in Statistics. A good knowledge of Statistics is of immense use in Economics and Actuarial Sciences and this course helps prepare you.The course starts with the definition of Moments and Skewness. You will learn about Moments of a distribution-There are 4 moments that are explained here. These are the Central Moments.Problems of the type-Calculate the first 4 central moments for 2,3,5,7,8 are discussed. You will also learn how to calculate the same for a frequency distribution. We then move on to Skewness. Skewness and Kurtosis is taught here.Skewness is defined as the lack of symmetry of a curve. Two types of skewness are discussed. Karl Pearson's coefficient of skewness is discussed. You will learn how to calculate Karl Pearson's coefficient of skewness for a frequency distribution. If the mean, mode and standard deviation of a frequency distribution are 27.5, 30, 7.2 respectively, calculate Karl Pearson's coefficient of skewness. Problems of this type are solved here.The next lesson teaches you more about Skewness. Bowley's coefficient of skewness is discussed. For a frequency distribution if the 3 quartiles are given, you will learn how to calculate Bowley's coefficient of skewness. You will be taught how to calculate Bowley's coefficient of skewness for a frequency distribution. Kurtosis is introduced here. We start with Kurtosis definition. Kurtosis is defined as a measure of the shape of the frequency curve. Mesokurtic, Leptokurtic and Platykurtic curves are discussed here. For a mesokurtic distribution , the standard deviation is 0.4. Calculate the 4th central moment. Problems of this type are discussed. If the first 4 central moments of a distribution are 0,2.4, 0.6 and 17.25. Examine the Skewness and Kurtosis of the distribution. This is another illustrated problem here.The last lesson is on Correlation and Rank Correlation. You will learn how to calculate the Correlation Coefficient. Correlation is defined as the relationship between two variables x and y. We start with the definition of Covariance. You will learn how to calculate covariance between 2 variables given their sum , product of sums and total number of variables. You are then introduced to Karl Pearson's coefficient of Correlation which helps to standardize the covariance formula. If the covariance of 2 variables is given , and the variance of the 2 variables is given, how will you find the correlation coefficient? Watch this lesson! You will be taught how to calculate Karl Pearson's coefficient of correlation for 2 variables x and y. If we give ranks to the two variables either in ascending or descending order, you get Spearman's Rank Correlation coefficient. How to calculate Spearman's Rank correlation coefficient for 2 variables is taught here. What happens if a rank is repeated? Watch this lesson to find out!Practice Problem Solving on Mean, Median, Mode and more!Get a basic introduction to Inferential Statistics. Learn basic terms such as sample mean, sample proportion and sample standard deviation. Also, learn what is interval estimation. You'll learn about confidence intervals and confidence values. How to calculate the interval estimation for the population mean and population proportion are taught here. It is useful to remember some standard confidence values which are explained here.Explore the magical world of hypothesis testing, where you'll learn about null hypothesis and various parameters for accepting or rejecting it.This is followed by t distributions , how to calculate the t values using the table and using the t values to accept or reject a hypothesis. You'll get an understanding of the two tailed t test.Enhance your learning today!
