Frequently, you can model a set of data with more than one distribution, or with a distribution that has one, two, or three parameters. For example, for each type of data, several distributions may be fit:
- Right-skewed data
- Often, you can fit either the Weibull or the lognormal distribution and obtain a good fit to the data.
- Symmetric data
- Often, you can fit the Weibull or the lognormal distribution. Sometimes, you can fit the normal distribution (depending on the heaviness of the tails) and obtain similar results.
- Left-skewed data
- Often, you can fit the Weibull or the smallest extreme value distribution.
A particular set of data can sometimes be modeled using either 2 or 3 parameters. A 3-parameter model can provide a better fit for some data, but can also result in overfitting the model. Overfitting means that the model fits the sample data well, but would not fit another sample from the same population. Usually, experts advise choosing the simplest model that works.
For more information on specific distributions that are used to model reliability data, go to the following topics: