The normal distribution arises in many areas of statistics.

Following are some of the most common situations in which the chi-squared distribution arises from a Gaussian-distributed sample.

This distribution arises in multivariate statistics as a derivative of the multivariate normal distribution.

Further distribution arises through its rhizomes which can develop extensive berry patches.

A long-tail distribution will arise with the inclusion of many values unusually far from the mean, which increase the magnitude of the skewness of the distribution.

If m approaches infinity as λ and σ are held constant, the normal distribution arises as a special case:

Rather, at these levels the distributions probably arise from evolutionary development centered on an underlying process of gene duplication.

A bimodal distribution most commonly arises as a mixture of two different unimodal distributions (i.e. distributions having only one mode).

Some investigators suggest that this distribution arises as a consequence of abnormal migration of germ cells during embryogenesis.

Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters.