The beta distribution is continuous. It is commonly used to represent variability over a fixed range. It can represent uncertainty in the probability of occurrence of an event. It is also used to describe empirical data and predict the random behavior of percentages and fractions and can be used to represent the reliability of a company’s devices.
Note: | Models that use beta distributions will run more slowly because of the inverse CDF and alternate parameter calculations that take place when random numbers are handled as part of beta distributions. |
The beta distribution is used under these conditions:
Minimum and maximum range is between 0 and a positive value.
Shape can be specified with two positive values, alpha and beta. If the parameters are equal, the distribution is symmetrical. If either parameter is 1 and the other parameter is greater than 1, the distribution is J-shaped. If alpha is less than beta, the distribution is said to be positively skewed (most of the values are near the minimum value). If alpha is greater than beta, the distribution is negatively skewed (most of the values are near the maximum value). Because the beta distribution is complex, the methods for determining the parameters of the distribution are beyond the scope of this manual. For more information about the beta distribution and Bayesian statistics, refer to the texts in the Bibliography.