Probability Distributions

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 bestfitting
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.
