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Student's Distribution

  If is a sample of size N drawn from a normal distribution with mean E(X) and variance , then


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