arma-thesis

Simulation modelling of irregular waves for marine object dynamics programmes
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transform.R (636B)

      1 arma.skew_normal_1 <- function(z, skewness, kurtosis) {
      2   (24 + 4*z*(-3 + z**2)* skewness + (3 - 6*z**2 + z**4)* kurtosis)/(24*(exp((z**2)/2)*sqrt(2*pi)))
      3 }
      4 
      5 arma.bits.erf <- function(x) {
      6   2 * pnorm(x * sqrt(2)) - 1
      7 }
      8 
      9 arma.bits.erfc <- function(x) {
     10   2 * pnorm(x * sqrt(2), lower = FALSE)
     11 }
     12 
     13 arma.bits.skewness_2 <- function(alpha) {
     14   (sqrt(2) * (4 - pi) * (alpha**3)) / (sqrt(pi + (pi-2) * (alpha**2))**3)
     15 }
     16 
     17 arma.bits.kurtosis_2 <- function(alpha) {
     18   (8*(-3 + pi)*(alpha**4))/ ((pi + (-2 + pi)*(alpha**2))**2)
     19 }
     20 
     21 arma.skew_normal_2 <- function(z, alpha) {
     22   arma.bits.erfc( -((z*alpha)/sqrt(2)) ) / (exp((z**2)/2)*sqrt(2*pi))
     23 }