Statistics Toolbox

tpdf

Student's t probability density function (pdf)

Syntax

• Y = tpdf(X,V)
  

Description

Y = tpdf(X,V) computes Student's t pdf at each of the values in X using the corresponding parameters in V. Vector or matrix inputs for X and V must have the same size. A scalar input is expanded to a constant matrix with the same dimensions as the other inputs. The degrees of freedom in V must be positive integers.

Student's t pdf is

Examples

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
  

See Also

pdf, tcdf, tinv, trnd, tstat

tinv

treedisp