This function finds the bivariate joint probability or the binary correlation from the corresponding Gaussian correlation x

This function finds the bivariate joint probability or the binary correlation from the corresponding Gaussian correlation x

omega(x = 0.5, p0_v1 = 0.5, p0_v2 = NA, correlation = FALSE)

Arguments

x: value of expected correlation between the corresponding Gaussian-distributed variables
p0_v1, p0_v2: probability of no precipitation occurrences for the v1 and v2 time series respectively. See Notes.
correlation: logical numeric value. Default is FALSE. If TRUE the function returns the binary correlation like eq. 6 of Mhanna, et al.,2011.

Value

probability of no precipitation occurrence in both v1 and v2 simultaneously. It is a matrix if x is a matrix.

Note

This function makes use of normal copula. A graphical introduction to this function (with its inverse) makes is present in Mhanna and Bauwens (2011) and Wilks (1988) (See fig. 1 and par. 3.2) If the argument p0_v2, the two marginal probability values must be given as a vector through the argument p0_v1: p0_v1=c(p0_v1,p0_v2) . In case x is a correlation/covariance matrix the marginal probabilities are given as a vector through the argument p0_v1.

References

D.S. Wilks (1998), Multisite Generalization of a Daily Stochastic Precipitation Generation Model, Journal of Hydrology, Volume 210, Issues 1-4, September 1998, Pages 178-191, https://www.sciencedirect.com/science/article/pii/S0022169498001863

Muamaraldin Mhanna and Willy Bauwens (2011) A Stochastic Space-Time Model for the Generation of Daily Rainfall in the Gaza Strip, International Journal of Climatology, Volume 32, Issue 7, pages 1098-1112, doi:10.1002/joc.2305 , https://rmets.onlinelibrary.wiley.com/doi/10.1002/joc.2305

Author

Emanuele Cordano

Examples

rho <- 0.4
p00 <- omega(x=rho,p0_v1=0.5,p0_v2=0.5)
cor00 <- omega(x=rho,p0_v1=0.5,p0_v2=0.5,correlation=TRUE)