Page 57 - MATLAB Recipes for Earth Sciences

48 3 Univariate Statistics

Probability Density Cumulative Distribution
Function Function
0.5 1
Φ=5 Φ=5
0.4 0.8
Φ=1

0.3 0.6
f(x) F(x)
0.2 0.4

0.1 0.2
Φ=1
0 0
−6 −4 −2 0 2 4 6 −6 −4 −2 0 2 4 6
x x
a b
Fig. 3.9 a Probability density function f(x) and b standardized (F(x) =1) cumulative
max
distribution function F(x) of a Student·s t distribution with different values for Φ.

which can be written as

if x>0. The single parameter Φ of the t distribution is the degrees of freedom.
In the analysis of univariate data, this parameter is Φ=n-1, where n is the
sample size. As Φ|’, the t distribution converges to the standard normal
distribution. Since the t distribution approaches the normal distribution for

Φ>30, it is not often used for distribution fitting. However, the t distribution
is used for hypothesis testing, namely the t–test (Chapter 3.7).

Fisher·s F Distribution

The F distribution was named after the statistician Sir Ronald Fisher
(1890-1962). It is used for hypothesis testing, namely for the F–test
(Chapter 3.8) (Fig. 3.10). The F distribution was named in honor of the
statistician Sir Ronald Fisher. The F distribution has a relatively com-