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Four Classes of Random Variables

Depending on the definition of a random variable, UNIPASS™ applies different methods for transformation from original space, X to standard normal space U:

• Statistically Independent (SI)
• Marginal with correlation coefficient matrix (MR)
• Conditional distributions (Hyper parametric distribution) on SI random variables
• Conditional distributions (Hyper parametric distribution) on MR random variables

Correlation Coefficient Matrix Definition Window

PDF Plot For Two MR Type Variables (Top View)

PDF Plot For Two MR Type Variables (3D View)

Conditional Random Variable Definition Window

PDF Plot of Conditional Random Variable

Hyper Parameter distributions accounts for the uncertainties in the parameters of distributions. They are useful whenever there is:

1. A limited amount of data
2. Poor quantification on physical bounds
3. A large amount of uncertainty in the most likely value (mean)

An example of Hyperparameterization is given below:

Random Variable: Rotor Speed

• Nominal Rotor Speed is 26,500 rpm

• 1/1000 minimum(i.e., -3s) rotor speed is 23500 rpm

• 1/1000 maximum (i.e., +3s) rotor speed is 29,500 rpm

• Due to mission to mission variation, the nominal (mean) rotor speed could vary uniformly between 25,000 rpm and 28,000 rpm

• Within a given mission, past data has suggested a normal distribution

From the preceding information, one can model the distribution of rotor speed as N(m, 1500) where the mean m is a Uniform distribution with 25,000 and 2800 as the lower and upper bounds, respectively. It is noted that it is incorrect to model the rotor speed as a marginal distribution. The correct and incorrect PDF of rotor speed are illustrated in the following figure.

 Example of Hyperparamerization

Last Updated 11/12/08

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