Page 53 - MATLAB Recipes for Earth Sciences
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44 3 Univariate Statistics
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 λ=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 floods. The probability density function is
and the cumulative distribution function is
The single parameter λ describes both the mean and the variance of this
distribution.
