R/RaoTest.R

In VecStatGraphs2D: Vector Analysis using Graphical and Analytical Methods in 2D

RaoTest <- function (azimuths, Alpha = 0.01) 
{ 
    TableRaoII <- matrix(c(247.32, 231.22, 221.14, 186.45, 168.02, 
        111.72, 61.48, 245.19, 232.98, 211.93, 183.44, 168.66, 
        116.3, 69.98, 236.81, 216.05, 206.79, 180.65, 166.3, 
        118.95, 76.52, 229.46, 211.57, 202.55, 177.83, 165.05, 
        121.13, 81.43, 224.41, 206.91, 198.46, 175.68, 163.56, 
        122.57, 85.23, 219.52, 203.17, 195.27, 173.68, 162.36, 
        123.74, 88.35, 215.44, 199.91, 192.37, 171.98, 161.23, 
        124.64, 90.95, 211.87, 197.04, 189.88, 170.45, 160.24, 
        125.38, 93.15, 208.69, 194.51, 187.66, 169.09, 159.33, 
        125.99, 95.05, 205.87, 192.25, 185.68, 167.87, 158.5, 
        126.5, 96.71, 203.33, 190.23, 183.9, 166.76, 157.75, 
        126.94, 98.17, 201.04, 188.39, 182.28, 165.75, 157.06, 
        127.32, 99.47, 198.96, 186.72, 180.81, 164.83, 156.43, 
        127.64, 100.64, 197.05, 185.19, 179.46, 163.98, 155.84, 
        127.93, 101.7, 195.29, 183.78, 178.22, 163.2, 155.29, 
        128.19, 102.67, 193.67, 182.48, 177.08, 162.47, 154.78, 
        128.42, 103.55, 192.17, 181.27, 176.01, 161.79, 154.31, 
        128.62, 104.36, 190.78, 180.15, 175.02, 161.16, 153.86, 
        128.81, 105.1, 189.47, 179.1, 174.1, 160.56, 153.44, 
        128.98, 105.8, 188.25, 178.11, 173.23, 160.01, 153.05, 
        129.13, 106.44, 187.11, 177.19, 172.41, 159.48, 152.68, 
        129.27, 107.04, 186.03, 176.32, 171.64, 158.99, 152.32, 
        129.4, 107.61, 185.01, 175.5, 170.92, 158.52, 151.99, 
        129.52, 108.13, 184.05, 174.73, 170.23, 158.07, 151.67, 
        129.63, 108.63, 183.14, 173.99, 169.58, 157.65, 151.37, 
        129.73, 109.1, 182.28, 173.29, 168.96, 157.25, 151.08, 
        129.82, 109.54, 181.45, 172.63, 168.38, 156.87, 150.8, 
        129.91, 109.96, 177.88, 169.74, 165.81, 155.19, 149.59, 
        130.28, 111.76, 174.99, 167.39, 163.73, 153.82, 148.6, 
        130.55, 113.2, 172.58, 165.44, 162, 152.68, 147.76, 130.76, 
        114.38, 170.54, 163.79, 160.53, 151.7, 147.05, 130.93, 
        115.37, 163.6, 158.13, 155.49, 148.34, 144.56, 131.44, 
        118.68, 159.45, 154.74, 152.46, 146.29, 143.03, 131.69, 
        120.62, 154.51, 150.69, 148.84, 143.83, 141.18, 131.94, 
        122.88, 151.56, 148.26, 146.67, 142.35, 140.06, 132.06, 
        124.21, 148.06, 145.38, 144.09, 140.57, 138.71, 132.19, 
        125.76, 145.96, 143.66, 142.54, 139.5, 137.89, 132.25, 
        126.68, 144.54, 142.48, 141.48, 138.77, 137.33, 132.29, 
        127.3, 143.48, 141.6, 140.7, 138.23, 136.91, 132.31, 
        127.76, 142.66, 140.93, 140.09, 137.8, 136.59, 132.33, 
        128.11, 142, 140.38, 139.6, 137.46, 136.33, 132.34, 128.4, 
        141.45, 139.93, 139.19, 137.18, 136.11, 132.35, 128.63, 
        140.99, 139.54, 138.84, 136.94, 135.92, 132.36, 128.83), 
        ncol = 7, byrow = TRUE)
    v = sort(azimuths)
    n = length(azimuths)
    Ti <- c(diff(v), 360 - (v[n] - v[1]))
    L <- 1/2 * sum(abs(Ti - 360/n))



    if ((n > 4)) {
        if (n <= 30) {
            Trow <- n - 3
        }
        else {
            if (n <= 32) {
                Trow <- 27
            }
            else {
                if (n <= 37) {
                  Trow <- 28
                }
                else {
                  if (n <= 42) {
                    Trow <- 29
                  }
                  else {
                    if (n <= 47) {
                      Trow <- 30
                    }
                    else {
                      if (n <= 62) {
                        Trow <- 31
                      }
                      else {
                        if (n <= 87) {
                          Trow <- 32
                        }
                        else {
                          if (n <= 125) {
                            Trow <- 33
                          }
                          else {
                            if (n <= 175) {
                              Trow <- 34
                            }
                            else {
                              if (n <= 250) {
                                Trow <- 35
                              }
                              else {
                                if (n <= 350) {
                                  Trow <- 36
                                }
                                else {
                                  if (n <= 450) {
                                    Trow <- 37
                                  }
                                  else {
                                    if (n <= 550) {
                                      Trow <- 38
                                    }
                                    else {
                                      if (n <= 650) {
                                        Trow <- 39
                                      }
                                      else {
                                        if (n <= 750) {
                                          Trow <- 40
                                        }
                                        else {
                                          if (n <= 850) {
                                            Trow <- 41
                                          }
                                          else {
                                            if (n <= 950) {
                                              Trow <- 42
                                            }
                                            else {
                                              Trow <- 43
                                            }
                                          }
                                        }
                                      }
                                    }
                                  }
                                }
                              }
                            }
                          }
                        }
                      }
                    }
                  }
                }
            }
        }

        if (sum(Alpha == c(0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 
            0.9)) == 0) {
            print("Alpha values are restricted to values 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, 0.9")
        }
        else {
            Tcol <- (1:7)[Alpha == c(0.001, 0.005, 0.01, 0.05, 
                0.1, 0.5, 0.9)]
            value <- TableRaoII[Trow, Tcol]
            if (value >= L) {
                print(paste("Rao Test: the hypothesis of uniformity is accepted for P =", Alpha))
            }
            else {
                print(paste("Rao Test: the hypothesis of uniformity is rejected for P =", Alpha))
            }
        }
    }
    else {
        print("Rao Test: Size of sample incorrect")
    }
}