omega_inv function

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,
  ...
)

Arguments

• p0: matrix of joint probabilities. Default is NULL, otherwise functions returns a matrix with values
• p0_v1, p0_v2: probablity of no precipitatin occurrences for the v1 and v2 time series respectively.
• p00: probability of no precipitation occurrence in both v1 and v2 simultanously returned by omega
• correlation: numerical value. DEfault is NA. Binary correlation retured by omega when the argumet correlation=TRUE (see omega_root)
• only.value: logical value. If TRUE (Default) the only Gaussian correletion (x input variable of omega) is returned, otherwise the complete output of uniroot is returned.
• interval: see interval option of uniroot. Default is c(-1,1).
• tolerance: tolerance (numeric) parameter used for comparisons with the extreme value of marginal probabilities. Default is 0.001.
• nearPD: logical. If TRUE (Default) a positive-definite correlation matrix is returned by applying nearPD in case p0 is a matrix and not NULL.
• force.independence: 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

Returns

value of expected correlation between the corresponding Gaussian-distributed variables (see x input argument of omega.

Note

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.

Examples

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)

See Also

normalCopula,pcopula,omega(and reference URLs therein)

Author(s)

Emanuele Cordano