eldo_user

Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
• The uniformly spaced probabilities p i =(i-1/2)/n where i=1, ..., n, the p i are the midpoints
of n contiguous probability intervals of width 1/n.
• The continuous strictly increasing piecewise-linear function joining the n points
(Y (i) ,p ι ):
where:
To avoid undefined denominators one must remove interior points in an interval of
constant output values.
Because is piecewise-linear, so is its inverse, and for a rank i such that , the
expression of inverse CDF is:
Coverage Intervals
A coverage interval for an output measure is an interval containing a known proportion of the
probability content of the distribution of that measure. That is a 100p% coverage interval for a
quantity Y with probability density function f Y is an interval [y low , y high ] for which:
We give in the .mcm file two different coverage intervals computed with the approximation
of the cumulative density function:
• The symmetric coverage interval defined as follows. Let α denote a value between 0 and
1 − p. The bounds of a 100p% coverage interval are obtained by linear inverse
interpolation.
To identify the lower endpoint such that
, we determine the rank r for
which the points and satisfy . Then by
interpolation:
Eldo® User's Manual, 15.3 487