fCopulae (version 3000.79)

t2d: Bivariate Student-t Distribution

Description

Density, distribution function, and random generation for the bivariate Student-t distribution.

Usage

pt2d(x, y = x, rho = 0, nu = 4)
dt2d(x, y = x, rho = 0, nu = 4)
rt2d(n, rho = 0, nu = 4)

Arguments

n

the number of random deviates to be generated, an integer value.

nu

the number of degrees of freedom, a numeric value ranging between two and infinity, by default four.

rho

the correlation parameter, a numeric value ranging between minus one and one, by default zero.

x, y

two numeric vectors defining the x and y coordinates.

Value

• pt2d returns a two column matrix of probabilities for the bivariate Student-t distribution function. dt2d returns a two column matrix of densities for the bivariate Student-t distribution function. rt2d returns a two column matrix of random deviates generated from the bivariate Student-t distribution function.

References

Azzalini A., (2004); The sn Package; R Reference Guide available from www.r-project.org. Venables W.N., Ripley B.D., (2002); Modern Applied Statistics with S, Fourth Edition, Springer.

Examples

## Bivariate Student-t Density:
   x = (-40:40)/10
   X = grid2d(x)
   z = dt2d(X$x, X$y, rho = 0.5, nu =6)
   Z = list(x = x, y = x, z = matrix(z, ncol = length(x)))
   persp(Z, theta = -40, phi = 30, col = "steelblue")