Bivariate Cauchy density

f(z1, z2) = c / (2 pi) (c^2 + z1^2 + z2^2)^(-3/2), the bivariate t with one degree of freedom and scale c^2 I (Mardia 1970, p. 86). Both marginals are Cauchy, yet E(Z2 | Z1) does not exist (Schabenberger & Gotway 2005, p. 293).

Usage

bvcchy(z1, z2, c = 1)

Arguments

z1, z2

Numeric evaluation points of equal length.

c

Scale, positive.

Value

Named list: density, c.

References

Mardia, K. V. (1970). Families of Bivariate Distributions. Hafner, p. 86. Schabenberger & Gotway (2005), Sec. 5.8, p. 293.

Examples

bvcchy(c(0, 0.5), c(0, -1.2), 1.5)
#> $density
#> [1] 0.07073553 0.03052580
#> 
#> $c
#> [1] 1.5
#>