# omega: This function finds the bivariate joint probability or the... In RGENERATEPREC: Tools to Generate Daily-Precipitation Time Series

## 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`.

Emanuele Cordano

## 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, http://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, http://dx.doi.org/10.1002/joc.2305

`normalCopula`,`pcopula`
 ```1 2 3``` ```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) ```