Chi-square distribution

1. Definition:

If n independent random variables ξ₁,ξ₂,...,ξn, are subject to the standard normal distribution (also known as independent distribution in the standard normal distribution), then this n the sum of squares of random variables which obey the standard normal distribution

constitute a new random change, the distribution of the law is called Chi-square distribution (chi-square distribution), recorded as:.

Chi-square distribution has one parameter called degrees of Freedom , just as the mean or variance in the normal distribution is another normal distribution, the difference of degrees of freedom is another chi-squared distribution. Recorded as:

，

Where, to limit the number of conditions.

Chi-square distribution is a new distribution constructed from normal distribution, and when the degree of freedom is very large, the chi-square distribution is approximate to normal distribution.

In the image above, Gamma () represents the gamma function.

2. Why are Chi-square distributions introduced?

The long-term result is stable and can be grasped clearly when the specific probability distribution is modeled as a certain situation. But what if there is a difference between expectation and fact. The deviation is a normal small amplitude fluctuation. or a modeling error. At this time, using chi-square distribution analysis results, to exclude suspicious results. "The use of chi-square distribution to verify the facts and expectations"

For more application descriptions of chi-square distribution, see:

Http://www.cnblogs.com/baiboy/p/tjx11.html