Graphics Programs Reference
In-Depth Information
Probability Density
Function
Cumulative Distribution
Function
1
1
σ=0.5
0.8
0.8
0.6
0.6
σ=1.0
0.4
0.4
σ=1.0
σ=2.0
σ=2.0
σ=0.5
0.2
0.2
0
0
0
2
4
6
0
2
4
6
x
x
a
b
Fig. 3.7 a
Probability density function
f
(
x
) and
b
standardized (
F
(
x
)
max
=1) cumulative
distribution function of a gaussian or normal distribution with mean µ=0 and different values
for standard deviation σ.
This defi nition of the normal distribution is often referred to as
z distribution
.
Logarithmic Normal or Log-Normal Distribution
The
logarithmic normal distribution
is used when the data have a lower
limit, e.g., the amount of precipitation or the frequency of earthquakes (Fig.
3.8). In such cases, distributions are usually characterized by signifi cant
skewness, which is best described by a logarithmic normal distribution The
probability density function of this distribution is
and the cumulative distribution function is
