Graphics Programs Reference
In-Depth Information
The cumulative distribution function is
where
The binomial distribution has two parameters
N
and
p
. The outcome of a
drilling program of oil provides an example of such distribution. Let us as-
sume that the probability of a drilling success is 0.1 or 10%. The probability
of
x
=3 wells out of a total number of
N
=10 wells is
Therefore only six out of one hundred wells are successful.
Poisson Distribution
When the numbers of trials is
N
|
and the success probability is
p
|
0, the
binomial distribution approaches the
Poisson distribution
with one single
parameter
=
Np
(Fig. 3.6) (Poisson, 1837). This works well for
N
>100 and
p
<0.05 or 5%. We therefore use the Poisson distribution for processes char-
acterized by extremely low occurrence, e.g., earthquakes, volcano eruptions,
storms and fl oods. The probability density function is
λ
and the cumulative distribution function is
The single parameter
λ
describes both the mean and the variance of this
distribution.
