Student's t probability density function
Y = tpdf(X,V)
Y = tpdf(X,V) computes Student's t pdf at each of the values in X using the corresponding degrees of freedom in V. X and V can be vectors, matrices, or multidimensional arrays that have the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs.
Student's t pdf is
The mode of the t distribution is at x = 0. This example shows that the value of the function at the mode is an increasing function of the degrees of freedom.
tpdf(0,1:6) ans = 0.3183 0.3536 0.3676 0.3750 0.3796 0.3827
The t distribution converges to the standard normal distribution as the degrees of freedom approaches infinity. How good is the approximation for v = 30?
difference = tpdf(-2.5:2.5,30)-normpdf(-2.5:2.5) difference = 0.0035 -0.0006 -0.0042 -0.0042 -0.0006 0.0035