Student's t probability density function
y = tpdf(x,nu)
y = tpdf(x,nu) returns the probability density function (pdf) of the Student's t distribution at each of the values in x using the corresponding degrees of freedom in nu. x and nu 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.
The mode of the Student's 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.
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 equal to 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
The probability density function (pdf) of the Student's t distribution is
where ν is the degrees of freedom and Γ( · ) is the Gamma function. The result y is the probability of observing a particular value of x from a Student's t distribution with ν degrees of freedom.