Extended Uniform Distribution Accounting for Uncertainty of Uncertainty

Increasingly, uncertainties are explicitly considered for important engineering tasks. Often, little case-specific information is available for characterizing these uncertainties. Uniform distributions are an easy way to describe errors in absence of more precise information. In many situations, the bounds are fixed based on user experience. The extended uniform distribution (EUD) provides a probability density function that accounts for higher orders of uncertainty (uncertainty of uncertainty) when using a uniform distribution to describe errors. Since the EUD accounts for several orders of uncertainty it is more representative than uniform and curvilinear distributions. The extended uniform distribution helps increase the reliability and robustness of tasks requiring uncertainty combination through better representing incomplete knowledge of parameters.