Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Aleatory uncertain variable  lognormal
This keyword is related to the topics:
Alias: none
Argument(s): INTEGER
Default: no lognormal uncertain variables
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required (Choose One)  Group 1  lambdas  First parameter of the lognormal distribution (option 3)  
means  First parameter of the lognormal distribution (options 1 & 2)  
Optional  lower_bounds  Specify minimum values  
Optional  upper_bounds  Specify maximium values  
Optional  initial_point  Initial values  
Optional  descriptors  Labels for the variables 
If the logarithm of an uncertain variable X has a normal distribution, that is , then X is distributed with a lognormal distribution. The lognormal is often used to model:
Within the lognormal uncertain optional group specification, the number of lognormal uncertain variables, the means, and either standard deviations or error factors must be specified, and the distribution lower and upper bounds and variable descriptors are optional specifications. These distribution bounds can be used to truncate the tails of lognormal distributions, which as for bounded normal, can result in the mean and the standard deviation of the sample data being different from the mean and standard deviation of the underlying distribution (see "bounded lognormal" and "bounded lognormaln" distribution types in[89]).
For the lognormal variables, one may specify either the mean and standard deviation of the actual lognormal distribution (option 1), the mean and error factor of the actual lognormal distribution (option 2), or the mean ("lambda") and standard deviation ("zeta") of the underlying normal distribution (option 3).
The conversion equations from lognormal mean and either lognormal error factor or lognormal standard deviation to the mean and standard deviation of the underlying normal distribution are as follows:
Conversions from and back to and or are as follows:
The density function for the lognormal distribution is:
When used with design of experiments and multidimensional parameter studies, distribution bounds are inferred. These bounds are [0, ].
For vector and centered parameter studies, an inferred initial starting point is needed for the uncertain variables. These variables are initialized to their means for these studies.