A company that manufactures electrical devices for custom orders wants to model the reliability of devices it produces. After analyzing the empirical data, the company knows that it can use the beta distribution to describe the reliability of the devices if the parameters are alpha = 10 and beta = 2.
The first step in selecting a probability distribution is matching the data with a distribution’s conditions. Checking the beta distribution:
These conditions match those of the beta distribution.
Figure 94, Beta distribution shows the beta distribution with the alpha parameter set to 10, the beta parameter set to 2, and Minimum and Maximum set to 0 and 1. The reliability rate of the devices will be x.
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.