Probability distributions are a fundamental concept in statistics.
They are used both on a theoretical level and a practical level.
Some practical uses of probability distributions are:
- To calculate confidence intervals for parameters
and to calculate critical regions for hypothesis tests.
- For univariate data, it is often useful to determine
a reasonable distributional model for the data.
- Statistical intervals and hypothesis tests are often
based on specific distributional assumptions. Before
computing an interval or test based on a distributional
assumption, we need to verify that the assumption
is justified for the given data set. In this case, the
distribution does not need to be the best-fitting
distribution for the data, but an adequate enough model
so that the statistical technique yields valid conclusions.
- Simulation studies with random numbers generated from
using a specific probability distribution are often needed.