Abstract
This paper compares the rate of convergence of the standard Hermite expansion and the less common Laguerre expansion to four beta distributions. With the exception of the arc sin variable, the simulated cumulative distribution based on polynomial chaos expansion can approach the target almost everywhere using 5 terms or less. However, the rate of convergence to the lower and upper bounds can be very slow. With regard to this aspect, the choice of the polynomial is important. For first-order reliability analysis, a simple 3-term Hermite expansion can provide an alternative to the Gaussian tail approximation approach for transforming non-Gaussian random variables into standard Gaussian random variables.