UnivRNG (version 1.2.3)

draw.t: Generates variates from standard t distribution

Description

This function implements pseudo-random number generation for a standard-\(t\) distribution with pdf

$$f(x|\nu)=\frac{\Gamma(\frac{\nu+1}{2})}{\Gamma(\frac{\nu}{2})\sqrt{\nu\pi}}(1+\frac{x^2}{\nu})^{-(\nu+1)/2}$$

for \(-\infty < x < \infty\) where \(\nu\) is the degrees of freedom.

Usage

draw.t(nrep,dof)

Arguments

nrep

Number of data points to generate.

dof

Degrees of freedom of the desired t distribution.

Value

A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.

References

Bailey, R. W. (1994). Polar generation of random variates with the t-distribution. Mathematics of Computation, 62, 779-781.

Examples

# NOT RUN {
draw.t(nrep=100000,dof=2)

draw.t(nrep=100000,dof=6)
# }