# t (Student) Distribution for the Probability Distribution Calculator

Density Function. The Student's t distribution has the probability density function (for n = 1, 2, . . .):

f(x) = G[(n+1)/2] / G(n/2) * (n*p)-1/2 * [1 + (x2/n)-(n+1)/2

where

 n is the shape parameter, degrees of freedom G is the Gamma function p is the constant Pi (3.14 . . .)

Distribution Function. The cumulative distribution function (the term was first introduced by Wilks, 1943) for the Student's t distribution depends on whether n is odd or even and is completely described in Evans, Hastings, and Peacock, 1993.

t. This field displays the current variate value for the Student's t distribution. When you edit this value (either manually or with the microscrolls), Statistica computes the associated p-value for the specified degrees of freedom.

p. This field displays the p-value computed from the specified variate value and degrees of freedom or you can enter a desired p-value (either manually or edit the existing value with the micro scrolls) and compute the critical value of the distribution for the specified degrees of freedom.

df. Specify here the shape parameter of the distribution, n. If this parameter is changed, then the p-value will be recomputed based on the respective variate value.