Editing Student's t-distribution (section)

===Robust parametric modeling===
The {{mvar|t}}&nbsp;distribution is often used as an alternative to the normal distribution as a model for data, which often has heavier tails than the normal distribution allows for; see e.g. Lange et al.<ref>{{cite journal|vauthors=Lange KL, Little RJ, Taylor JM|date=1989|title=Robust Statistical Modeling Using the {{mvar|t}} Distribution|url=https://cloudfront.escholarship.org/dist/prd/content/qt27s1d3h7/qt27s1d3h7.pdf|journal=[[Journal of the American Statistical Association]]|volume=84|issue=408|pages=881–896|doi=10.1080/01621459.1989.10478852|jstor=2290063}}</ref> The classical approach was to identify [[outlier (statistics)|outliers]] (e.g., using [[Grubbs's test]]) and exclude or downweight them in some way. However, it is not always easy to identify outliers (especially in [[curse of dimensionality|high dimensions]]), and the {{mvar|t}}&nbsp;distribution is a natural choice of model for such data and provides a parametric approach to [[robust statistics]].

A Bayesian account can be found in Gelman et al.<ref>{{cite book|title=Bayesian Data Analysis|vauthors=Gelman AB, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB|publisher=CRC Press|year=2014|isbn=9781439898208|location=Boca Raton, Florida|pages=293|chapter=Computationally efficient Markov chain simulation|display-authors=3}}</ref> The degrees of freedom parameter controls the kurtosis of the distribution and is correlated with the scale parameter. The likelihood can have multiple local maxima and, as such, it is often necessary to fix the degrees of freedom at a fairly low value and estimate the other parameters taking this as given. Some authors{{Citation needed|date=June 2015}} report that values between 3 and 9 are often good choices. Venables and Ripley{{Citation needed|date=June 2015}} suggest that a value of 5 is often a good choice.