This function is the inverse of omega function
omega_inv(
p0 = NULL,
p0_v1 = 0.5,
p0_v2 = p0_v1,
p00 = p0_v1 * p0_v2,
correlation = NA,
only.value = TRUE,
interval = c(-1, 1),
tolerance = 0.001,
nearPD = TRUE,
force.independence = TRUE,
...
)matrix of joint probabilities. Default is NULL, otherwise functions returns a matrix with values
probablity of no precipitatin occurrences for the v1 and v2 time series respectively.
probability of no precipitation occurrence in both v1 and v2 simultanously returned by omega
numerical value. DEfault is NA. Binary correlation retured by omega when the argumet correlation=TRUE (see omega_root)
logical value. If TRUE (Default) the only Gaussian correletion (x input variable of omega) is returned,
otherwise the complete output of uniroot is returned.
see interval option of uniroot. Default is c(-1,1).
tolerance (numeric) parameter used for comparisons with the extreme value of marginal probabilities. Default is 0.001.
logical. If TRUE (Default) a positive-definite correlation matrix is returned by applying nearPD in case p0 is a matrix and not NULL.
logical value. Default is TRUE. If it is TRUE, no negative corelation is considered and negative values of correletion are forced to be 0 (independence).
further arguments for uniroot
value of expected correlation between the corresponding Gaussian-distributed variables (see x input argument of omega.
This function finds the zero of the omega_root function by calling uniroot.
If the argument p0 is not NULL and is a matrix of joint probabilities, the function returns a correlation matrix by using the elements of p0 ass joint probabilities for each couple and p0_v1 as a vector of marginal probability of each occurrence/no-occurrence
(In this case if the length of p0_v1 does not correspond to the number of columns of p0, the marginal probabilities are taken from the diagonal of p0).
See the R code for major details.
normalCopula,pcopula,omega(and reference URLs therein)
x <- omega_inv(p0_v1=0.5,p0_v2=0.5,p00=1.1*0.5*0.5)
omega(x,p0_v1=0.5,p0_v2=0.5)
#> [1] 0.2749996