and

are estimators of the mean *E*(*X*) and of the variance of the estimator . The quotient

is described by Student's distribution (also called the *t*-distribution)
with *f*=*N*-1 degrees of freedom. Its probability density is

where denotes Euler's gamma function. The *t*-distribution has the properties

For it approaches the standard normal distribution.

Rudolf K. Bock, 7 April 1998