Geoscience Reference
In-Depth Information
ans =
11.1788
ans =
13.5108
Here, the values for
p
are calculated from the complement of ~68%, which
is ~32%, halved on both tails of the Gaussian distribution, e.g.,
(1-0.6827)/2
and
1-(1-0.6827)/2
.
h e standard deviation ˃ of the Gaussian distribution is important for
the dei nition of coni dence intervals. In many examples, however, the
coni dence of one sigma (ʼ±1˃) or ~68% that the true value falls within
the ʼ±1˃ range is not sui cient and higher coni dence intervals such as two
sigma (ʼ±2˃) and three sigma (ʼ±3˃) intervals are therefore also used. We
can calculate the corresponding probabilities that the true value falls within
the ʼ±2˃ range and the ʼ±3˃ range by typing
sum(pdf(find(x>mu-2*sigma,1,'first'):find(x<mu+2*sigma,1,'last')))
sum(pdf(find(x>mu-3*sigma,1,'first'):find(x<mu+3*sigma,1,'last')))
which yields
ans =
0.9545
ans =
0.9973
or ~95% and ~99%. Again, using
norminv
we can calculate the upper and
lower bounds of the two sigma (ʼ±2˃) range
norminv(0.05/2,mu,sigma)
norminv(1-0.05/2,mu,sigma)
which yields
ans =
10.0595
ans =
14.6301
and the three sigma (ʼ±3˃) range
norminv(0.01/2,mu,sigma)
norminv(1-0.01/2,mu,sigma)
which yields
ans =
9.3414
ans =
15.3482
