A continuous distribution described by the probability density function of the form

for −∞ < x < ∞ and ν‎ = 1,2,…. The parameter ν‎ is called the number of degrees of freedom. It has mean zero for ν‎ > 1 and variance ν‎/(ν‎−2) for ν‎ > 2. As ν‎ gets large the t-distribution converges to the standard normal distribution. The square of a variable with a t-distribution with ν‎ degrees of freedom has an F-distribution with (1, ν‎) degrees of freedom. Cauchy distribution is a particular case of t-distribution with ν‎ = 1. The moment generating function for t-distribution is undefined, as there is no interval around t = 0 where it is finite.