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

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Description

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

Usage

1
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 occurences 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 occurence 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 the following URL references: http://onlinelibrary.wiley.com/doi/10.1002/joc.2305/abstract and http://www.sciencedirect.com/science/article/pii/S0022169498001863 (See fig. 1 and par. 3.2) If the argument p0_v2, the two marginal probabily 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.

Author(s)

Emanuele Cordano

See Also

normalCopula,pcopula

Examples

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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)