Unformatted text preview: enerates random
numbers following lognormal distribution and the two input parameters used to
characterize the distribution are expectation and standard deviation of the corresponding
normal distribution.
Also, when dealing with samples/observations from a random variable following
lognormal distribution, geometric mean and geometric standard deviation are commonly
given: g ( X ) exp( ) g ( X ) exp( )
It can be shown that the geometric mean of a lognormal distribution is its median, and is
smaller than its actual mean (or arithmetic mean).
Note:
Geometric mean of a data series: Geometric standard deviation: 3 Two random variables:
joint CDF
joint CDF ∬ ( ) )( )] Independence: X and Y are independent if and only {
Expectation:
[
=∫
[ Covariance: ∫ [{
[ [ If
[ [ But uncorrelated [ independent! Dependence does not mean correlation. Random Vector:
[ Covariance Matrix:
[ [ ∑[ [ 4 [ MonteCarlo Simulation Repeated random sampling to capture effects due to uncertainties in inputs. key point is random number generation. Require (joint) probability distributions, however, this may be difficult to get in
reality. In LCA, independence is usually assumed, but mass/energy conservation
has to be applied as constrains. Other known equations may also be applied.
Uniform, Lognormal, and triangular distributions are most commonly used.
Ma...
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 Fall '07
 Staff
 Normal Distribution, Probability theory, probability density function, Cumulative distribution function, MonteCarlo Simulation

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