A SIMPLE METHOD FOR ESTIMATING THE PARAMETERS OF THE BETA DISTRIBUTION APPLIED TO MODELING UNCERTAINTY IN GAS TURBINE INLET TEMPERATURE

摘要

The beta distribution is a particularly convenient model for random variables when only the minimum, maximum and most likely values are available. It is also very useful for estimating the mean and standard deviation given this information. In this paper a simple method is proposed to estimate the beta parameters from these three values. The proposed method has advantages over the conventional approach. In the conventional approach, the four parameters of the beta distribution are determined from only three values by assuming a standard deviation that is one-sixth the range. In contrast, the new method assumes a value for one of the beta shape parameters based on an analogy with the normal distribution. This new approach allows for a very simple algebraic solution of the beta shape parameters in contrast to the simultaneous solution required by the conventional method. The results of the proposed method are very similar to the conventional method. However, the proposed method generally gives a slightly higher (more conservative) estimate of the standard deviation when the distribution is skewed. In addition, the new approach allows the standard deviation to vary as the shape or skew of the distribution varies. Both methods were applied to modeling the probability distribution of temperature in a gas turbine inlet.