Learn more about Statistics Toolbox

Student's t Distribution

On this page…
Definition Background Example See Also

Definition

Student's t pdf is

where Γ( · ) is the Gamma function.

Back to Top

Background

The t distribution is a family of curves depending on a single parameter ν (the degrees of freedom). As ν goes to infinity, the t distribution approaches the standard normal distribution.

W. S. Gossett discovered the distribution through his work at the Guinness brewery. At the time, Guinness did not allow its staff to publish, so Gossett used the pseudonym "Student."

If x is a random sample of size n from a normal distribution with mean μ, then the statistic

where is the sample mean and s is the sample standard deviation, has Student's t distribution with n – 1 degrees of freedom.

Back to Top

Example

The plot compares the t distribution with ν = 5 (solid line) to the shorter tailed, standard normal distribution (dashed line).

x = -5:0.1:5;
y = tpdf(x,5);
z = normpdf(x,0,1);
plot(x,y,'-',x,z,'-.')

Back to Top

See Also

Continuous Distributions (Statistics)

Back to Top

Rician Distribution

t Location-Scale Distribution

© 1984-2009- The MathWorks, Inc.    -   Site Help   -   Patents   -   Trademarks   -   Privacy Policy   -   Preventing Piracy   -   RSS