8.1 Estimating a Population Mean Point Estimate estimate  a single number, or point. 因为:the mean of the sample mean equals the population mean (μx¯ = μ). 所以:In other words, on average, the sample mean equals the population mean.(即mean of sample mean…

95%置信区间.置信区间的两端被称为置信极限.对一个给定情形的估计来说,置信水平越高,所对应的置信区间就会越大. 对置信区间的计算通常要求对估计过程的假设(因此属于参数统计),比如说假设估计的误差是成正态分布的…

什么是置信区间 置信区间又称估计区间,是用来估计参数的取值范围的.常见的52%-64%,或8-12,就是置信区间(估计区间).   置信区间的概述 1.对于具有特定的发生概率的随机变量,其特定的价值区间:一个确定的数值范围(“一个区间”). 2.在一定置信水平时,以测量结果为中心,包括总体均值在内的可信范围. 3.该区间包含了参数θ真值的可信程度.                                4.参数的置信区间可以通过点估计量构造,也可以通过假设检验构造. 关于置信区间的宽窄…

无偏估计是参数的样本估计量的期望值等于参数的真实值. 一个简单的例子(https://www.zhihu.com/question/22983179/answer/23470969): 比如我要对某个学校一个年级的上千个学生估计他们的平均水平(真实值,上帝才知道的数字),那么我决定抽样来计算. 我抽出一个10个人的样本,可以计算出一个均值.那么如果我下次重新抽样,抽到的10个人可能就不一样了,那么这个从样本里面计算出来的均值可能就变了,对不对? 因为这个均值是随着我抽样变化的,而我抽出哪10个人…

Source: Sigma Zone, by Philip Mayfield The Binomial Distribution is commonly used in statistics in a variety of applications. Binomial data and statistics are presented to us daily. For example, in the election of political officials we may be asked…

Sampling and Estimation Sampling Error Sampling error is the difference between a sample statistic(the mean, variance, or standard deviation of the sample) and its corresponding population parameter(the true mean, variance, or standard deviation of t…

Confidence Intervals for One Population Mean When σ Is Known Obtaining Confidence Intervals for a Population Mean When σ Is Known The z-interval procedure works reasonably well even when the variable is not normally distributed and the sample size is…

Previously in this series: The beta distribution Empirical Bayes estimation Credible intervals The Bayesian approach to false discovery rates Bayesian A/B testing Beta-binomial regression Understanding empirical Bayesian hierarchical modeling Mixture…

scipy.stats Scipy的stats模块包含了多种概率分布的随机变量,随机变量分为连续的和离散的两种.所有的连续随机变量都是rv_continuous的派生类的对象,而所有的离散随机变量都是 rv_discrete的派生类的对象. This module contains a large number of probability distributions as well as a growing library of statistical functions. Each univ…

Multiple Regression What is multiple regression? Multiple regression is regression analysis with more than one independent variable. It is used to quantify the influence of two or more independent variables on a dependent variable. The general multip…