Chi Distribution

In probability theory and statistics, the chi distribution is a continuous probability distribution. It is the distribution of the square root of the sum of squares of independent random variables having a standard normal distribution. The most familiar example is the Maxwell distribution of (normalized) molecular speeds which is a chi distribution with 3 degrees of freedom (one for each spatial coordinate). If are k independent, normally distributed random variables with means and standard deviations, then the statistic

is distributed according to the chi distribution. The chi distribution has one parameter: which specifies the number of degrees of freedom (i.e. the number of ).