- RContinuousRandomVariable

- Models > Parameter > Random Variable > Continuous

- Name of the object in Rt
- Allowable characters are upper-case and lower-case letters, numbers, and underscore (“_”).
- The name is unique and case-sensitive.

- Current realization of the random variable

- Probability distribution of the random variable
- The distribution type is followed by the distribution parameters inside parentheses.
- These parameters, respectively, correspond to Parameter 1 to Parameter 4 that appear as some other properties below.
- If, for instance, only two parameters appear inside parentheses for a particular distribution type, only Parameter 1 and Parameter 2 are applicable to that distribution.
- If the “User-defined” distribution is selected, two more properties are shown, namely, X Points and PDF Points, described below.

- Mean of the random variable
- It can be a number or another parameter.
- If changed, the values of Coefficient Of Variation and Parameter 1 to Parameter 4 properties are re-calculated.

- Standard deviation of the random variable
- It can be a number or another parameter.
- If changed, the values of Coefficient Of Variation and Parameter 1 to Parameter 4 properties are re-calculated.

- Coefficient of variation of the random variable
- It is a standardized measure of dispersion of a probability distribution.
- If changed, the values of Standard Deviation and Parameter 1 to Parameter 4 properties are re-calculated.

- The first parameter of the random variable, as appears inside the parentheses in the Distribution Type.
- If changed, the values of Mean, Standard Deviation, and Coefficient Of Variation properties are re-calculated.

- The second parameter of the random variable, as appears inside the parentheses in the Distribution Type, if applicable.
- If changed, the values of Mean, Standard Deviation, and Coefficient Of Variation properties are re-calculated.

- The third parameter of the random variable, as appears inside the parentheses in the Distribution Type, if applicable.
- If changed, the values of Mean, Standard Deviation, and Coefficient Of Variation properties are re-calculated.

- The fourth parameter of the random variable, as appears inside the parentheses in the Distribution Type, if applicable.

- Indicates whether the random variable describes an “Aleatory” or an “Epistemic” uncertainty.
- This is employed, for instance, when computing model response standard deviation sensitivities in FORM.
- For more information, see Der Kiureghian (2009)

- Vector of random variable realizations for which the PDF values are given to the property below, i.e., PDF Points in a “User Defined” distribution.

- Vector of PDF values of the random variable realizations that are given to the property above, i.e., X Points in a “User Defined” distribution.

- Element of the \(\boldsymbol{\alpha}\) importance vector, computed in FORM, that corresponds to this random variable.
- \(\boldsymbol{\alpha}\) is a unit vector that indicates the relative importance of the random variables involved in a FORM analysis when correlations are neglected/non-existent.
- For more information, see Der Kiureghian (2005).

- Element of the \(\boldsymbol{\gamma}\) importance vector, computed in FORM, that corresponds to this random variable.
- \(\boldsymbol{\gamma}\) is a unit vector that indicates the relative importance of the random variables involved in a FORM analysis when correlations are considered.
- For more information, see Der Kiureghian (2005).

- Element of the FOSM importance vector, \(\boldsymbol{\omega}\), computed in FOSM, that corresponds to this random variable.
- \(\boldsymbol{\omega}\) is a unit vector that indicates the relative importance of the random variables involved in a FOSM analysis.
- For more information, see Der Kiureghian (2005).
- \(\boldsymbol{\omega}\) is computed as $$\boldsymbol{\omega}\ = - {\nabla {g^T}{\mathbf{D _ X}} \over {\left\| {\nabla {g^T}{\mathbf{D_X}}} \right\|}}$$ where \(\nabla {g}\) = gradient of the limit-state function, \(g\), and \(\mathbf{D_X}\) = standard deviation matrix of random variables, \(\mathbf{X}\).

- Element of the \(\boldsymbol{\delta}\) sensitivity vector, that corresponds to this random variable.
- \(\boldsymbol{\delta}\) is a dimensionless vector that is computed by multiplying the standard deviation matrix by the gradient of the reliability index with respect to the mean of random variables.
- For more information, see Der Kiureghian (2005).

- Element of the \(\boldsymbol{\eta}\) sensitivity vector, that corresponds to this random variable
- \(\boldsymbol{\eta}\) is a dimensionless vector that is computed by multiplying the standard deviation matrix by the gradient of the reliability index with respect to the standard deviation of random variables
- For more information, see Der Kiureghian (2005)

- Element of the \(\boldsymbol{\kappa}\) sensitivity vector, that corresponds to this random variable.
- \(\boldsymbol{\kappa}\) is a dimensionless vector equal to the gradient of the reliability index with respect to the coefficient of variation of random variables.

- Derivative of the reliability index, \({\beta}\), with respect to the mean of this random variable

- Derivative of the reliability index, \({\beta}\), with respect to the standard deviation of this random variable

- Removes the object.

- Plots the probability density function of the random variable in the range of mean ± three standard deviations.

- Plots the cumulative distribution function of the random variable in the range of mean ± three standard deviations.

- Plots the inverse cumulative distribution function of the random variable in the range of mean ± three standard deviations

- Prints the probability density function value for a given random variable realization on the output pane.

- Prints the cumulative distribution function value for a given random variable realization on the output pane.

- Prints the inverse cumulative distribution function value, i.e., the realization, for a given probability on the output pane.

- Beta Distribution
- Chi-Squared Distribution
- Exponential Distribution
- Gamma Distribution
- Gumbel Distribution
- Laplace Distribution
- Logisitic Distribution
- Lognormal Distribution
- Normal Distribution
- Rayleigh Distribution
- t Distribution
- Uniform Distribution
- Weibull Distribution
- Wald Distribution
- Levy Distribution
- Irwin-Hall Distribution
- Birnbaum-Saunders Distribution
- Type-2 Gumbel Distribution
- Pareto Distribution
- F Distribution
- Arcsine Distribution

- Der Kiureghian, A. (2005). First-and second-order reliability methods. In E. Nikolaidis, D. M. Ghiocel, & S. Singhal (Eds.), Engineering design reliability handbook. Boca Raton, Florida: CRC Press
- Der Kiureghian, A., & Ditlevsen, O. (2009). Aleatory or epistemic? Does it matter? Structural Safety, 31(2), 105–112