Geoscience Reference
In-Depth Information
a
b
Fig. 3.6
Probability density function
f
(
x
) of a Poisson distribution with dif erent values for ʻ:
a
ʻ=0.5, and
b
ʻ=2.
Poisson Distribution
When the number of trials is
N
→∞ and the success probability is
p
→0,
the binomial distribution approaches a
Poisson distribution
with a single
parameter ʻ=
Np
(Fig. 3.6) (Poisson 1837). h is works well for
N
>100 and
p
<0.05 (or 5%). We therefore use the Poisson distribution for processes
characterized by extremely low occurrence, e.g., earthquakes, volcanic
eruptions, storms and l oods. h e probability density function is
and the cumulative distribution function is
h e single parameter ʻ describes both the mean and the variance of this
distribution.
Normal or Gaussian Distribution
When
p
=0.5 (symmetric, no skew) and
N
→∞, the binomial distribution
approaches a
normal
or
Gaussian distribution
dei ned by the mean ʼ and
standard deviation ˃ (Fig. 3.7). h e probability density function of a normal
