Student's t-distribution

StudentT(dof)

The Student-T distribution describes the deviation of a sample mean from the true mean when the samples are generated by a normally distributed process. The statistic

t = (m - u)/(s*Sqrt(n))

where m is the sample mean, u the actual mean, s the sample standard deviation, and n the sample size, is distributed according to the Student-T distribution with n - 1 degrees of freedom. The parameter, «dof», is the degrees of freedom. Student-T distributions are bell-shaped, much like a normal distribution, but with heavier tails, especially for smaller degrees of freedom. When n = 1, it is known as the Cauchy distribution. For efficiency reasons, when a latin-hypercube sampling method is selected, psuedo-latin-hypercube method is used to sample the Student-T, which samples from the T-distribution, but does not guarantee a perfect latin spread of the samples.

Parameter Estimation

If you want to estimate the parameter from sample data X indexed by I, you can use the following estimation formula provided that Variance(X, I) > 1:

«dof» := 2*Variance(X, I)/(Variance(X, I) - 1)

Example

See Also

• Variance
• Normal
• Dens_StudentT
• CumStudentT
• Parametric continuous distributions
• Distribution Densities Library