Getting Started

GETTING STARTED WITH ARENA
Lognormal(, ): LOGNORMAL(LogMean, LogStd) or LOGN(LogMean, LogStd)
Probability
Density
Function
Denote the user-specified input parameters as
LogMean = l and LogStd = l .
Then let
and
the probability density function can then be
written as
f(x) = for x > 0
0 otherwise
Parameters
Mean LogMean ( l > 0) and standard deviation LogStd ( l > 0) of the lognormal
random variable. Both LogMean and LogStd must be specified as strictly positive
real numbers.
Range
[0, +
Mean LogMean = 1 = e + 2 2
Variance (LogStd) 2 = 2 1 = e 2 +
2
e 2 – 1
Applications
The lognormal distribution is used in situations in which the quantity is the product of
a large number of random quantities. It is also frequently used to represent task times
that have a distribution skewed to the right. This distribution is related to the normal
distribution as follows. If X has a lognormal ( l , l ) distribution, then ln(X) has a
normal (, ) distribution. Note that and are not the mean and standard deviation
of the lognormal random variable X, but rather the mean and standard deviation of
the normal random variable lnX.
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