Geoscience Reference
In-Depth Information
Student's t Distribution
h e
Student's t distribution
was i rst introduced by William Gosset (1876-
1937) who needed a distribution for small samples (Fig. 3.9). Gosset was
an employee of the Irish Guinness Brewery and was not allowed to publish
research results. For that reason he published his
t
distribution under the
pseudonym
Student
(Student 1908). h e probability density function is
where ʓ is the Gamma function
which can be written as
if
x
>0. h e single parameter ʦ of the
t
distribution is the number of degrees
a
b
Fig. 3.9 a
Probability density function
f
(
x
), and
b
cumulative distribution function
F
(
x
), of a
Student's
t
distribution with two dif erent values for ʦ.
