Statistics 简明教程
Statistics - Chi-squared Distribution
自由度为 k 的卡方分布(卡方分布或 ${X^2}$ - 分布)是 k 个独立标准正态随机变量平方和的分布。它是统计学中使用最广泛的概率分布之一。它是伽马分布的一种特殊情况。
The chi-squared distribution (chi-square or ${X^2}$ - distribution) with degrees of freedom, k is the distribution of a sum of the squares of k independent standard normal random variables. It is one of the most widely used probability distributions in statistics. It is a special case of the gamma distribution.

卡方分布被统计学家广泛用于计算以下内容:
Chi-squared distribution is widely used by statisticians to compute the following:
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Estimation of Confidence interval for a population standard deviation of a normal distribution using a sample standard deviation.
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To check independence of two criteria of classification of multiple qualitative variables.
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To check the relationships between categorical variables.
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To study the sample variance where the underlying distribution is normal.
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To test deviations of differences between expected and observed frequencies.
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To conduct a The chi-square test (a goodness of fit test).
Probability density function
卡方分布的概率密度函数给出为:
Probability density function of Chi-Square distribution is given as: