Chi-squared distribution
Probability distribution and special case of gamma distribution / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Chi-square distribution?
Summarize this article for a 10 year old
In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals.[2][3][4][5] This distribution is sometimes called the central chi-squared distribution, a special case of the more general noncentral chi-squared distribution.
Probability density function | |||
Cumulative distribution function | |||
Notation | or | ||
---|---|---|---|
Parameters | (known as "degrees of freedom") | ||
Support | if , otherwise | ||
CDF | |||
Mean | |||
Median | |||
Mode | |||
Variance | |||
Skewness | |||
Excess kurtosis | |||
Entropy | |||
MGF | |||
CF | [1] | ||
PGF |
The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in finding the confidence interval for estimating the population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks.