Three-Parameter Student distribution | Vose Software

Three-Parameter Student distribution

Format: Student3(μ,σ,n)

Examples of two Student3 distributions are given below:


The Student3 (or 3-parameter Student) distribution is similar to the Student-t distribution, but it allows for more flexibility as the mean can be different from zero and the standard deviation is specified as a parameter and thus not dependent on the number of degrees of freedom (ν) as in the case of a Student distribution.

The 3-parameter Student distribution is used in situations to model variables that look normally distributed, but have longer tails (meaning a higher probability of seeing more extreme values) than the Normal distribution.


The Student3 distribution is obtained from the classical Student distribution by rescaling and shifting it in order to have a mean and standard deviation as specified.

ModelRisk functions added to Microsoft Excel for the Three-Parameter Student-T distribution

VoseStudent3 generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseStudent3Object constructs a distribution object for this distribution.

VoseStudentProb returns the probability density or cumulative distribution function for this distribution.

VoseStudentProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseStudentFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseStudentFitObject constructs a distribution object of this distribution fitted to data.

VoseStudentFitP returns the parameters of this distribution fitted to data.


Three-Parameter Student distribution equations