pcuseries {simecol}

Generate Plackett Bivariate Random Numbers

Description

Generate bivariate uniform random numbers according to the Plackett distribution.

Usage

pcu(x, alpha = rho2alpha(rho), rho)
pcuseries(n, alpha = rho2alpha(rho), rho, min = 0, max = 1)
alpha2rho(alpha)
rho2alpha(rho)

Arguments

n

number of observations.

x

vector of uniformly [0, 1] distributed real numbers.

alpha

association coefficient of the Plackett distribution.

rho

Pearson correlation coefficient.

min, max

lower and upper limits of the distribution. Must be finite.

Details

The functions can be used to generate bivariate distributions with uniform marginals. Function pcu generates a vector of uniform random values of length(x) which are correlated to the corresponding vector x, pcuseries generates an auto-correlated series, and alpha2rho resp. rho2alpha convert between the Pearson correlation coefficient and the association measure of the Plackett distribution.

References

Johnson, M., Wang, C., & Ramberg, J. (1984). Generation of multivariate distributions for statistical applications. American Journal of Mathematical and Management Sciences, 4, 225-248.

Nelsen, R. B. (2006). An Introduction to Copulas. Springer, New York.

See Also

runif

Examples

x <- runif(100)
y <- pcu(x, rho = 0.8)
plot(x, y)
cor(x, y)

x <- pcuseries(1000, rho=0.8)
plot(x, type="l")
acf(x)
pacf(x)