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t Location-Scale Distribution


The t location-scale distribution has the density function

with location parameter µ, scale parameter σ > 0, and shape parameter ν > 0. If x has a t location-scale distribution, with parameters µ, σ, and ν, then

has a Student's t distribution with ν degrees of freedom.


The t location-scale distribution is useful for modeling data distributions with heavier tails (more prone to outliers) than the normal distribution. It approaches the normal distribution as ν approaches infinity, and smaller values of ν yield heavier tails.


To estimate distribution parameters, use mle or the Distribution Fitting app.

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