In probability theory and statistics, the chi distribution is a continuous probability distribution. The distribution usually arises when a k-dimensional vector’s orthogonal components are independent and each follow a standard normal distribution. The length of the vector will then have a chi distribution. The most familiar example is the Maxwell distribution of (normalized) molecular speeds which is a chi distribution with 3 degrees of freedom.

Probability distribution function of the Chi distribution is:

f(x,a,b,v) = exp (- ( ( x-a )/b )^2/2 )* ( (x-a)/b )^( v-1 )/( 2^( v/2-1 ) * b*gamma( v/2 ) )

support a < x ⇐ Inf